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A 
CLASS ROOM LOGIC 

DEDUCTIVE AND INDUCTIVE 



WITH SPECIAL APPLICATION TO 
THE SCIENCE AND ART OF TEACHING 



BY 



GEORGE HASTINGS McNAIR, Ph. D. 

HEAD OF DEPARTMENT OF LOGIC AND MATHEMATICS, CITY TRAINING 
SCHOOL FOR TEACHERS. JAMAICA. NEW YORK CITY 



THE ETHLAS PRESS 

FIVE NORTH BROADWAY. NYACK. NEW YORK 



BC 101 

.Ms 



COPTRIGHT, 1914, BY 

George Hastings McNaib 



DEC 15 1914 
©C1A391484 



5fa 

MY WIFE. 



PREFACE. 

This treatise is an outgrowth of our class room work 
in logic. 

It has been published in the hope of removing some of 
the difficulties which handicap the average student. 

We trust that the language is simple and definite and 
that the illustrative exercises and diagrams may be help- 
ful in making clear some of the more abstruse topics. 

If a speedy review for examination is necessary, it is 
recommended that the briefer course as outlined on page 
493 be followed and that the summaries closing each 
chapter be carefully read. 

Only the fundamentals of deductive and inductive logic 
have received attention. Moreover emphasis has been 
given to those phases which appear to commend them- 
selves because of their practical value. 

Further than this we trust that the book may fulfill in 
some small way the larger mission of inspiring better 
thinking and, in consequence, of leading to a more 
serviceable citizenship. 

Surely as civilization advances it is with the expecta- 
tion of giving greater significance to the assumption "that 
man is a rational animal." 

I am indebted to a number of writers on logic, notably 
to Mill, Lotze, Keynes, Hibben, Fowler, Aikins, Hyslop, 
Creighton and Jevons. I am likewise under obligation to 



Vlll PREFACE 

that large body of students who, by frankly revealing 
their difficulties, have given me a different point of view. 
For constructive criticism and definite encouragement 
I owe a personal debt of gratitude to Prof. Charles Gray 
Shaw of New York University, to Prof. Frank D. 
Blodgett of the Oneonta Normal School and to Prin. 
A. C. MacLachlan of the Jamaica Training School for 
Teachers. 



G. H. McN. 



City Training School for Teachers, 
Jamaica, N. Y. City. 
October 3, 1914. 



TABLE OF CONTENTS 

Page 

Chapter 1. — The Scope and Nature of Logic ... 1 

The Mind, 1. Logic Related to Other Subjects, 2. 
Logic Defined, 3. The Value of Logic to the Student, 
5. Outline, 7. Summary, 7. Review Questions, 8. 
Questions for Original Thought and Investigation, 9. 

Chapter 2. — Thought and Its Operation .... 10 

The Knowing Mind Compared with the Thinking 
Mind, 10. Knowing by Intuition, 11. The Thinking 
Process, 12. Notions, Individual and General, 14. 
Knowledge and Idea as Related to the Notion, 15. 
The Logic of the Psychological Terms Involved in 
the Notion, 16. Thought in the Sensation and Percept, 
18. Evolution and the Thinking Mind, 19. The Con- 
cept as a Thought Product, 21. The Judgment as a 
Thought Product, 22. Inference as a Thought Prod- 
uct, 24. Thinking and Apprehension, 24. Stages in 
Thinking, 25. Outline, 26. Summary, 27. Review 
Questions, 29. Questions for Original Thought and 
Investigation, 30. 

Chapter 3. — The Primary Laws of Thought ... 32 

Two Fundamental Laws, 32. The Law of Identity, 
32. The Law of Contradiction, 35. The Law of Ex- 
cluded Middle, 39. The Law of Sufficient Reason, 

40. Unity of Primary Laws of Thought, 40. Outline, 

41. Summary, 42. Illustrative Exercises, 43. Review 
Questions, 44. Questions for Original Thought and 
Investigation, 45. 

ix 



X CONTENTS 

Page 
Chapter 4. — Logical Terms 47 

Logical Thought and Language Inseparable, 47. 
Meaning of Term, 47. Categorematic and Syncate- 
gorematic Words, 48. Singular Terms, 49. General 
Terms, 49. Collective and Distributive Terms, 50. 
Concrete and Abstract Terms, 51. Connotative and 
Non-connotative Terms, 52. Positive and Negative 
Terms, 53. Contradictory and Opposite Terms, 53. 
Privative and Nego-positive Terms, 55. Absolute and 
Relative Terms, 56. Outline, 57. Summary, 57. Illus- 
trative Exercises, 58. Review Questions, 59. Ques- 
tions for Original Thought and Investigation, 60. 

Chapter 5. — The Extension and Intension of Terms . 62 

Two-fold Function of Connotative Terms, 62. Ex- 
tension and Intension Defined, 63. Extended Com- 
parison of Extension and Intension, 63. A List of 
Connotative Terms Used in Extension and Intension, 
65. Other Forms of Expression for Extension and 
Intension, 66. Law of Variation in Extension and In- 
tension, 66. Important Facts in Law of Variation, 69. 
Law of Variation Diagrammatically Illustrated, 70. 
Outline, 72. Summary, 72. Illustrative Exercises, 73. 
Review Questions, 75. Questions for Original 
Thought and Investigation, 76. 

Chapter 6. — Definition 77 

Importance, 77. The Predicables, 77. The Nature 
of a Definition, 82. Definition and Division Compared, 
84. The Kinds of Definitions, 85. When the Three 
Kinds of Definitions are Serviceable, 87. The Rules 
of Logical Definition, 88. Terms Which Cannot be 
Defined Logically, 93. Definitions of Common Edu- 
cational Terms, 94. Outline, 97. Summary, 98. Illus- 
trative Exercises, 100. Review Questions, 102. Ques- 
tions for Original Thought and Investigation, 103. 



CONTENTS XI 

Page 
Chapter 7. — Logical Division and Classification . . 105 

Nature of Logical Division, 105. Logical Division 
Distinguished from Enumeration, 106. Logical Divi- 
sion as Partition, 107. Four Rules of Logical Divi- 
sion, 108. Dichotomy, 110. Classification Compared 
with Division, 112. Kinds of Classification, 113. Two 
Rules of Classification, 114. Use of Division and 
Classification, 114. Outline, 115. Summary 116. Re- 
view Questions, 117. Questions for Original Thought 
and Investigation, 118. 

Chapter 8. — Logical Propositions 120 

The Nature of Logical Propositions, 120. Kinds of 
Logical Propositions, 121. The Four Elements of a 
Categorical Proposition, 122. Logical and Grammatical 
Subject and Predicate Distinguished, 125. The Four 
Kinds of Categorical Propositions, 126. Propositions 
which do not Conform to Logical Type, 129. Propo- 
sitions not Necessarily Illogical, 138. The Relation 
between Subject and Predicate, 140. Outline, 150. 
Summary, 151. Illustrative Exercises, 154. Review 
Questions, 156. Questions for Original Thought and 
Investigation, 157. 

Chapter 9. — Immediate Inference — Opposition . . .159 

The Nature of Inference, 159. Immediate and Medi- 
ate Inference, 159. The Forms of Immediate Infer- 
ence, 161. (1) Opposition, 161. 

Chapter 10. — Immediate Inference (Continued) . . 170 

Immediate Inference by Obversion, 170. Immediate 
Inference by Conversion, 176. Immediate Inference by 
Contraversion, 181. Epitome of the Four Processes 
of Immediate Inference, 182. Inference by Inversion, 
183. Outline, 183. Summary, 183. Illustrative Exer- 
cises, 185. Review Questions, 189. Problems for 
Original Thought and Investigation, 190. 



Xll CONTENTS 

Page 
Chapter 11. — Mediate Inference — The Syllogism . . 192 
Inference and Reasoning, 192. The Syllogism, 192. 
The Rules of the Syllogism, 193. Rules of Syllogism 
Explained, 194. Aristotle's Dictum, 208. Canons of 
the Syllogism, 209. Mathematical Axioms, 210. Out- 
line, 210. Summary, 211. Illustrative Exercises, 213. 
Review Questions, 215. Questions for Original Thought 
and Investigation, 216. 

Chapter 12. — Figures and Moods of the Syllogism . 218 
The Four Figures of the Syllogism, 218. The Moods 
of the Syllogism, 221. Testing the Validity of the 
Moods, 223. Special Canons of the Four Figures, 
226. Special Canons Related, 233. Mnemonic Lines, 
234. Relative Value of the Four Figures, 239. Out- 
line, 240. Summary, 241. Illustrative Exercises, 243. 
Review Questions, 245. Questions for Original Thought 
and Investigation, 245. 

Chapter 13. — Incomplete Syllogisms and Irregular 

Arguments . . . . . . 247 

Enthymeme, 247. Epicheirema, 249. Polysyllogisms. 
Prosyllogism — Episyllogism, 250. Sorites, 251. Ir- 
regular Arguments, 258. Outline, 259. Summary, 260. 
Review Questions, 261. Questions for Original Thought 
and Investigation, 261. 

Chapter 14. — Categorical Arguments Tested According 

to Form 263 

Arguments of Form and Matter, 263. Order of Pro- 
cedure in a Formal Testing of Arguments, 263. Il- 
lustrative Exercise in Testing Arguments which are 
Complete and whose Premises are Logical, 265. Illus- 
trative Exercise in Testing Completed Arguments, one 
or both of whose Premises are Illogical, 269. Incom- 
plete and Irregular Arguments, 277. Common Mis- 
takes of the Student, 281. Outline, 281. Summary, 
282. Review Questions, 283. Questions for Original 
Thought and Investigation, 285. 



CONTENTS XI 11 

Page 

Chapter 15. — Hypothetical and Disjunctive Arguments 

Including the Dilemma . . . 288 

Three Kinds of Arguments, 288. Hypothetical 
Arguments, 288. Antecedent and Consequent, 289. 
Two Kinds of Hypothetical Arguments, 290. Rule and 
Two Fallacies of Hypothetical Argument, 291. 
Hypothetical Arguments Reduced to Categorical Form, 
293. Illustrative Exercises Testing Hypothetical Argu- 
ments of All Kinds, 297. Disjunctive Arguments, 302. 
Two Kinds of Disjunctive Arguments, 302. First Dis- 
junctive Rule, 303. Second Disjunctive Rule, 306. 
Reduction of Disjunctive Argument, 307. The Di- 
lemma, 308. Four Forms of Dilemmatic Arguments, 
309. The Rule of Dilemma, 311. Illustrative Exer- 
cises Testing Disjunctive and Dilemmatic Argument, 
311. Ordinary Experiences Related to Disjunctive 
Proposition and Hypothetical Argument, 313. Out- 
line, 315. Summary, 316. Review Questions, 318. 
Questions for Original Thought and Investigation, 320. 

Chapter 16. — The Logical Fallacies of Deductive 

Reasoning 322 

A Negative Aspect, 322. Paralogism and Sophism, 
322. A Division of the Deductive Fallacies, 323. Gen- 
eral Divisions Explained, 325. Fallacies of Immediate 
Inference, 326. Fallacies in Language (Equivocation), 
328. Fallacies in Thought (Assumption), 334. Out- 
line, 344. Summary, 345. Illustrative Exercises in 
Testing Arguments in Both Form and Meaning, 349. 
Review Questions, 350. Questions for Original Thought 
and Investigation, 353. 

Chapter 17. — Inductive Reasoning 355 

Inductive and Deductive Reasoning Distinguished, 
355. The "Inductive Hazard," 356. Complexity of the 
Problem of Induction, 358. Various Conceptions of 



XIV CONTENTS 

Page 

Induction, 359. Induction and Deduction Contiguous 
Processes, 360. Induction an Assumption, 361. Uni- 
versal Causation, 361. Uniformity of Nature, 362. 
Inductive Assumptions Justified, 364. Three Forms 
of Inductive Research, 365. Induction by Simple 
Enumeration, 367. Induction by Analogy, 368. Induc- 
tion by Analysis, 373. Perfect Induction, 375. Tra- 
duction, 377. Outline, 379. Summary, 380. Review 
Questions, 383. Questions for Original Thought and 
Investigation, 384. 

Chapter 18. — Mill's Five Special Methods of Obser- 
vation and Experiment .... 386 

Aim of Five Methods, 386. Method of Agreement, 
387. Method of Difference, 393. The Joint Method of 
Agreement and Difference, 397. The Method of Con- 
comitant Variations, 402. The Method of Residues, 
406. General Purpose and Unity of Five Methods, 
409. Outline, 411. Summary, 412. Review Ques- 
tions, 414. Questions for Original Thought and In- 
vestigation, 416. 

Chapter 19. — Auxiliary Elements in Induction. Obser- 
vation — Experiment — Hypothesis . 418 

Foundation of Inductive Generalizations, 418. Ob- 
servation, 419. Experiment, 419. Rules for Logical 
Observation and Experiment, 420. Common Errors 
of Observation and Experiment, 423. The Hypothesis, 
425. Induction and Hypothesis Distinguished, 426. 
Hypothesis and Theory Distinguished, 427. The Re- 
quirements of a Permissible Hypothesis, 427. Uses of 
Hypothesis, 429. Characteristics Needed by Scientific 
Investigators, 431. Outline, 432. Summary, 433. Re- 
view Questions, 435. Questions for Original Thought 
and Investigation, 435. 



CONTENTS XV 

Page 
Chapter 20. — Logic in the Class Room .... 437 
Thought is King, 437. Special Functions of Induc- 
tion and Deduction, 438. Two Types of Minds, 438. 
Conservatism in School, 439. The Method of the Dis- 
coverer, 440. Real Inductive Method not in Vogue in 
Class Room Work, 444. As a Method of Instruction, 
Deduction Superior, 446. Conquest, not Knowledge, the 
Desideratum, 447. Motivation as Related to Spirit of 
Discovery, 449. Discoverer's Method Adapted to Class 
Room Work, 450. Question and Answer Method not 
Necessarily One of Discovery, 457. Outline, 458. 
Summary, 459. Review Questions, 461. Questions for 
Original Thought and Investigation, 462. 

Chapter 21. — Logic and Life 463 

Logic Given a Place in a Secondary Course, 463. 
Man's Supremacy Due to Power of Thought, 463. Im- 
portance of Progressive Thinking, 465. Necessity of 
Right Thinking, 466. Indifferent and Careless Thought, 
467. The Rationalization of the World of Chance, 468. 
The Rationalization of Business and Political Sophis- 
tries, 470. The Rationalization of the Spirit' of Prog- 
ress, 471. A Rationalization of the Attitude Toward 
Work, 474. The Logic of Success, 475. Outline, 477. 
Summary, 478. Review Questions, 479. Questions for 
Original Thought and Investigation, 480. 

General Exercises in Testing Categorical Arguments . 481 

General Exercises in Testing Hypothetical, Disjunctive 

and dllemmatic arguments . . 484 

Examination Questions for Training Schools and'Col- 

leges 486 

Bibliography 492 

Outline of Briefer Course 493 

Index 495 



CHAPTER 1. 

THE SCOPE AND NATURE OF LOGIC. 

1. THE MIND. 

As to the true conception of matter the world is igno- 
rant. Yet when asked, "What does matter do ?" the reply 
is, "Matter moves, matter vibrates." Moreover, relative 
to the exact nature of mind, the world is likewise ignorant. 
But to the question, "What does mind do?" the response 
comes, "The Mind knows, the mind feels, the mind wills.'' 
The mind has ever manifested itself in these three ways. 
Because of this three-fold function it is easy to think of 
the mind as being separated into distinct compartments, 
each constituting an independent activity. This is erro- 
neous. The mind is a living unit having three sides but 
never acting one side at a time. When the mind knows it 
also feels in some way and wills to some extent. To illus- 
trate : Music is heard and one knows it to be Rubinstein's 
Melody in F. The execution being good one feels pleas- 
ure. That the pleasurable state may be augmented one 
wills a listening attitude. For analytical purposes the 
psychologists have a way of naming the state of mind 
from the predominating manifestation. 

2. LOGIC RELATED TO OTHER SUBJECTS. 

What the mind is may in time be answered satis- 
factorily by philosophy; what the mind does is de- 
scribed by psychology ; what the mind knows is treated by 
logic. Again: the mind as a whole furnishes the subject 



2 The Scope and Nature of Logic 

matter for psychology, whereas logic is concerned with 
the mind knowing, aesthetics with the mind feeling, and 
ethics with the mind willing. Ethics attempts to answer 
the question, "What is right?" aesthetics, "What is beau- 
tiful?" and logic, "What is true?" 

Though both psychology and logic treat of the knowing 
aspect of the mind, yet the fields are not identical. The 
former deals with the process of the knowing mind as a 
whole, while the latter is concerned mainly with the 
product of the knowing mind when it thinks. To be spe- 
cific: The mind knows when it becomes aware of any- 
thing, moreover, this condition of awareness appears in 
two ways : first, immediately or by intuition; second, after 
deliberation or by thinking. For example, one may know 
immediately or by intuition that the object in the hand is 
a lead pencil, but when requested to state the length of 
the pencil there is deliberation involving a comparison of 
the unknown length with a definite measure. It may now 
finally be asserted that the pencil is six inches long. 
When we know without hesitation the process involved is 
intuition, whereas when the knowledge comes after some 
sort of comparison the mental act is called thinking. It, 
therefore, becomes the business of psychology to deal with 
both intuition and thinking while logic devotes its atten- 
tion to thinking only, and even in this field the work of 
logic is more or less indirect. The specific scope of logic 
is the product of thinking or thought.* What are the 



♦Note. Sometimes thinking and thought are used interchangeably. 
This is confusing. Properly, " thinking " is always a process of the 
knowing mind while " thought " is the product of this process, just 
as the flour of the gristmill is the product of the grinding process. 



Logic Related to Other Subjects 3 

forms of thought? What are the laws of thought? Are 
the several thoughts true ? These are the questions which 
logic is supposed to answer. 

For the logician thought has two sources, his own 
mind and the mind of others. In the latter case thought 
becomes accessible through the medium of language. 
There is in consequence a close connection between logic, 
the science of thought, and grammar, the science of 
language. Because of this near relation logic is some- 
times called the "grammar of thought/' 

To study any science properly one must have thoughts 
and since logic is the science of all thought the subject 
may be regarded as the science of sciences. 

3. LOGIC DEFINED. 

"Logic is the science of thought." This definition com- 
monly given is too brief to be helpful. Should not a defi- 
nition of any subject represent a working basis upon 
which one may build with some knowledge of what the 
structure is to be? The following, a little out of the ordi- 
nary, seems to supply this condition: Logic as a science 
makes known the laws and forms of thought and as an art 
suggests conditions which must be fulfilled to think rightly. 

In justification of the latter definition it may be argued 
that it covers the topics usually treated by logicians. 
It is said that a science teaches us to know while an art 
teaches us to do. As a science logic teaches us to know 
certain laws which underlie right thinking. For example, 
the law of identity which makes possible all affirmative 
judgments, such as "Some men are wise/' "All metals are 



4 The Scope and Nature of Logic 

elements," etc. Likewise as a science logic acquaints us 
with certain universal forms to which thought shapes 
itself, such as definitions, classifications, inductions, de- 
ductions. Further, logic lays down definite rules which 
lead to right thinking. To wit: Because it is true of a 
part of a class it should not be assumed that it is true of 
the whole of that class: or, in short, do not distribute 
an undistributed term. 

A possible profit to the student may result from a study 
of certain authentic definitions herewith subjoined: 

(i) "Logic is the science of the laws of thought." 
Jevons. 

(2) "Logic is the science which investigates the 
process of thinking." Creighton. 

(3) "Logic as a science aims to ascertain what are the 
laws of thought; as an art it aims to apply these laws to 
the detection of fallacies or for the determination of 
correct reasoning." Hyslop. 

(4) "Logic is the art of thinking." Watts. 

(5) "Logic is the science and also the art of thinking." 
Whateley. 

(6) "Logic is the science of the formal and necessary 
laws of thought." Hamilton. 

(7) "Logic is the science of the regulative laws of the 
human understanding." Ueberweg. 

(8) "Logic treats of the nature and of the laws of 
thought." Hibben. 

(9) "Logic may be defined as the science of the conditions 
on which correct thoughts depend, and the art of attaining 
to correct and avoiding incorrect thoughts." Fowler. 



Logic Defined 5 

(10) "Logic is the science of the operations of the 
understanding which are subservient to the estimation of 
evidence." Mill. 

(n) "Logic may be briefly described as a body of 
doctrines and rules having reference to truth." Bain. 

It would seem as if there were as many different defini- 
tions as there are books on the subject. This is due partly 
to the disposition of the older logicians to ignore the art 
of logic and partly to the difficulty of giving in a few 
words a satisfactory description of a broad subject. In 
the fundamentals of logical doctrine present-day authori- 
ties virtually agree. 

4. THE VALUE OF LOGIC TO THE STUDENT. 

Logic is rapidly coming into favor as a major subject 
in institutions devoted to educational theory. Some of 
the reasons for this change of attitude are herewith 
subjoined: 

(i) Logic should stimulate the thought powers. This 
is the age of the survival of the thinker. The fact that 
the man who thinks best is the man who thinks much and 
carefully will be accepted by those who believe that prac- 
tice makes perfect. "One needs only to observe the aver- 
age commuter to conclude that a large percent, of our 
business men read too much and think too little." "Much 
readee and no thinkee" was the reply of a Chinaman when 
asked his opinion of the doings of the average American. 
"We as a people are newspaper mad, reading for enter- 
tainment, seldom for mental improvement." 

(2) Logic aims to secure correct thought. Are not 



6 The Scope and Nature of Logic 

many of the sins and most of the failures in this world 
due to incorrect thinking? 

(3) Logic should train to clear thinking. It would be 
difficult to estimate the loss of energy to the brain worker 
because he has not the power to think clearly. Maxi- 
mum efficiency is impossible with a befogged brain. How 
discouraging it is to the student to attempt to get from 
the paragraph the thought of the author, who in trying 
to be profound succeeds in being profoundly abstruse. 
There is a probable need for broad, deep thoughts, but 
these when placed in a text book should be sharpened to 
a point. 

(4) Logic should aid one to estimate aright the state- 
ments and arguments of others. This is of especial value 
to the teacher who is constrained to teach largely from 
text books. Because it is found in a book is not proof 
positive that it is true. Why should we assume that the 
book is infallible when we know that the man behind the 
book is fallible? 

(5) Logic insists on definite, systematic procedure. To 
be logical is to be businesslike. A study of logic would, 
no doubt, benefit our churches and parliamentary orders 
as well as our schools. 

(6) Logic demands lucid, pointed, accurate expression. 
How we would increase our working efficiency could we 
but express our thoughts in an attractive and interesting 
manner. To listen to the speeches of some of our great 
and good men who are concerned in directing the "ship of 
state" is sufficient argument that the American schools 
need more logic. 



The Value of Logic to the Student 7 

(7) Logic is especially adapted to a general mental 
training. Despite the swing of the pendulum of public 
opinion toward the bread-and-butter side of life, there 
are many of high repute who claim that for the sake of 
that mental acumen which distinguished the Greek 
from his contemporaries we cannot afford to sacrifice 
everything on the altar of commercialism. 

(8) Logic worships at the shrine of truth and adds to 
our store of knowledge. . What has aided the world more 
in its march onward than this deep-seated passion for 
truth and what has impeded it more than that vain and 
wanton indifference to truth which brought to the world 
its darkest age? 

5. OUTLINE— 

The Scope and Nature of Logic. 

(1) The Mind. 

Three aspects. 
Unity of 

(2) Logic Related to Other Subjects. 

Mental philosophy, psychology, logic. 
Psychology, logic, aesthetics, ethics. 
Two ways of knowing. 
Special province of logic. 
Logic and language. 
A science of sciences. 

(3) Logic Defined. 

A general definition. 

A more satisfactory definition. 

A list of authentic definitions. 

(4) The Value of Logic to the Student. 

Eight reasons for its study. 

6. SUMMARY. 

(1) The aspects of the mind are knowing, feeling and willing. 



8 The Scope and Nature of Logic 

The mind is a living unit and never knows without feeling in 
some way and willing to some extent. 

(2) What the mind is must be answered by philosophy; what 
the mind does by psychology and what the mind knows by 
logic. 

Psychology treats of the mind as a whole, logic of the mind 
knowing, aesthetics of the mind feeling and ethics of the mind 
willing. Ethics answers the question, What is right ? Aesthetics, 
What is beautiful? Logic, What is true? 

The standpoint of logic is not identical with any particular por- 
tion of psychology. 

The mind knows in two ways : (a) by intuition, (b) by think- 
ing. Thinking is a process — thought a product. Logic deals in- 
directly with the former and directly with the latter. 

Generally speaking, logic is a systematic study of thought. For 
the logician thought has two sources : (a) his own mind and 
(b) spoken or written language. 

Because of the ambiguity of language logic has much to do 
with it as a faulty vehicle of thought. 

(3) Logic as a science makes known the laws and forms of 
thought and as an art suggests conditions which must be fulfilled 
to think rightly. Author. 

"Logic may be defined as the science of the conditions on which 
correct thoughts depend, and the art of attaining to correct and 
avoiding incorrect thoughts." Fowler. 

In the fundamentals of logical doctrine present day logicians 
virtually agree. 

(4) Logic should stimulate the thought powers; secure correct 
and clear thinking; aid in the estimation of arguments; inspire 
definite, systematic procedure; demand lucid, pointed, accurate 
expresssion and be especially adapted to general mental discipline. 

Logic adds to our store of knowledge and develops a passion 
for the truth. 

7. REVIEW QUESTIONS. 

(1) Explain and illustrate the three ways in which the mind 
may manifest itself. 

(2) Illustrate the fact that the mind acts in unity. 






Review Questions 



(3) Show briefly how logic is related to mental philosophy, 
psychology, aesthetics, ethics and grammar. 

(4) Illustrate the two ways of knowing. 

(5) Distinguish between thinking and thought. 

(6) Give a general definition of logic. Why is this definition 
unsatisfactory? 

(7) What are the two sources of thought? 

(8) Why are logic and language so closely related? 

(9) Give that definition of logic which best satisfies you. 

(10) Summarize the benefits which you hope to derive from 
your study of logic. 

(11) Why should teachers be clear thinkers? 

(12) Why should teachers be especially on guard against 
incorrect statements of all kinds? 

(13) Show how logic might be of assistance to the business 
man. 

8. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTI- 
GATION. 

(1) Prove that there is nothing real in the world save the 
mind itself. 

(2) "Logic is concerned primarily with how we ought to think 
and only in a secondary way with how we actually think." 
Explain this quotation. 

(3) Prove that there is no such thing as intuitive knowing. 

(4) Is there any difference between knowledge and thoughts? 
Illustrate. 

(5) Show by illustrations that the English language is ambig- 
uous. 

(6) Prove by concrete illustration that this is the age of the 
survival of the thinker. 

(7) Which is the more harmful: falsehood mixed with truth 
or unadulterated falsehood? Give reasons. 

(8) Give a concrete example of incorrect thinking. 

(9) Show that wrong thinking leads to wrong doing. 

(10) To be worth while must every subject have a practical 
value ? 

(11) "The 20th century virtue is a passion for truth." Prove 
the truth of this. 



CHAPTER 2. 



THOUGHT AND ITS OPERATION. 



1. THE KNOWING MIND COMPARED WITH THE THINK- 
ING MIND. 

In the preceding chapter we were told that the mind 
may know in two ways (i) by intuition and (2) by think- 
ing. It is thus implied that the knowing mind includes 
the thinking mind plus intuition. Thinking always in- 
volves knowing, but knowing need not involve thinking, 
and when some logicians maintain that to know a thing 
one must think it, there is danger of being misled. They 
mean by this that in order to know anything in a perma- 
nent and highly serviceable way one must think it. All 
animals know, even such a stupid one as the oyster, and 
yet one would hardly give an oyster credit for thinking. 
Only the higher orders of animal life think. Some argue 
that the power is confined exclusively to the human fam- 
ily. This opinion is debatable. If the claimant means by 
thinking, reasoning then his ground is well taken. But if 
he is willing to give to thinking a broader content, then he 
has little defense for his stand. However, attach as broad I 
a meaning to thinking as the derivation of the word will I 
permit and even then it is a narrower term than knowing. 
Thinking plus intuition equals knowing, and in intuition 
there is probably no thinking. 

10 



Knowing by Intuition II 

2. KNOWING BY INTUITION. 

It has been aff rmed that intuition is the process involved 
when the mind knows instantly* 

Illustrations : 

(i) As I raise my eyes a figure comes to view. My 
mind knows instantly that it is the figure three. (2) The 
ear catches immediately a tune which is being sung in 
the room below. Without deliberation the mind recog- 
nizes the tune as America. The mind may thus know by 
intuition through any one of the five senses. These are 
the wires of connection between the outer world and the 
mind within and transmission over these wires may be 
instantaneous or intuitive. This is not all. (3) My mind 
may center its attention on itself and may recognize there 
a mental picture or image of a pet dog. Since this activ- 
ity is without any apparent deliberation the process must: 
be intuitive. To define intuitive knowledge as that which 
comes to the mind through the senses only is incorrect, 
as it leaves out altogether the knowledge the mind may 
obtain of its own activity as in illustration "(3)." 

Knowledge is anything known. Intuitive knowledge is 
knowledge which comes to the mind immediately by direct 
observation. The field for intuitive knowledge may be 
the external world or the internal world though, of 
course, the former is the more common ground. It is 
here that the mind by intuition secures the most of its raw 
material which, through the process of thinking, is worked 
over into a connected, unified system of lasting value. 



•Intuitive knowing might be termed habitual knowing. 



12 Thought and Its Operation 

The intuitions are the beginning and the basis of ail 
knowledge, and knowledge gained by intuition is the basis 
of all thinking. 

3. THE THINKING PROCESS. 

It is claimed that think comes from the same root as 
thick. From this one would conclude that the process of 
thinking is virtually a process of thickening. Surely as 
one thinks he enriches or thickens his knowledge. As one 
thinks percepts into concepts and concepts into judgments 
he makes richer in meaning the various notions con- 
cerned. Thinking is largely a matter of pressing many 
into one: of linking together the disconnected fragments 
of the conscious field. 

Definition : 

Thinking is the deliberative process of affirming or 
denying connections. 

The same idea may be expressed in a variety of ways 
as the following indicate. 

( i) "Thinking is the conscious adjustment of a means 
to an end in problematic situations." Miller. 

(2) "To think is to designate an object through a 
mark or attribute or what is the same thing, to determine 
a subject through a predicate." Bowen. 

(3) "Thought is the comprehension of a thing under 
a general notion or attribute." Wm. Hamilton. 

(4) "To think is to make clear through concepts the 
perceived objects." Dressier. 

In the foregoing definitions it is implied that thinking 
is a connecting or thickening process. In all forms of 



The Thinking Process 13 

thinking from the simplest to the most complex the know- 
ing mind hunts for some basis of connection and having 
found it thinks the relationship into a unified whole. 

The thinking process is the digestive process of the 
mind. Much as the digestive organs assimilate the food 
stuff of the physical world, so the thinking organ assim- 
ilates the food stuff of the mental world. 

Illustrations of the Thinking Process : 

(1) The child is unable to explain the meaning of 
"hocus-pocus" as it occurs in the question, "What hocus- 
pocus is this ?" The child mind is unable to establish any 
connection between the word and its real meaning. In 
short, is unable to think into it a meaning; it therefore 
becomes necessary for the teacher to establish some basis 
of connection and this he does by suggesting nonsense 
as a synonym. 

(2) The teacher holds before the class an Egyptian 
house god and asks, "What is it?" After a moment of 
hesitation some child who has seen pictures of "his satanic 
majesty" avers that the object is a "little devil." Thus 
has a connection been established between the idol and 
pictures of satan. 

(3) John is unable to solve the following problem as 
he can discern no connection between the data given and 
the data required. Problem. 3/4 of my salary is $900, 
what is my salary? 

Data. Given : 3/4 of salary = $900. 
Required : 4/4 of salary = ? 



14 Thought and Its Operation 

In order that John may think a solution the teacher 
must lead him to see some connection between 3/4 and 4/4. 
With this in mind the form of the data is changed to 

Given: 3-fourths = $900 

Required: 4- fourths = ? 
or 

Given: 3 parts = $900 

Required: 4 parts = ? 
John now notes that 4 parts is 4/3 times 3 parts and con- 
sequently writes 4/3 of $900, which is $1,200 as the an- 
swer. Or he may find the value of 1 part and then of 
4 parts. 

4. NOTIONS, INDIVIDUAL AND GENERAL. 

A notion is any product of the knowing mind — any- 
thing which the mind notes or becomes aware of. 

But the mind knows in two ways, by intuition and by 
thinking. In consequence the mind has two kinds of 
notions, those which are intuitive or individual notions 
and those which originally result from thinking or 
general notions. 

An individual notion is a notion of one thing. A gen- 
eral notion is a notion of a class of things. 

Note. Here it is necessary to distinguish between a 
thing and an object. An object is a thing which occupies 
space such as a pencil or a book. "Thing" is, therefore, a 
broader term than "object." "A thing is that which has 
individual existence." From the viewpoint of logic 
"thing" includes objects, qualities, relations, spiritual 



Notions, Individual and General 15 

entities. Gravitation is a thing but not an object. A 
tree is both an object and a thing. 

Illustrations of Notions. 

My notion of the pencil with which I am writing is an 
individual notion, but my notion of pencil as a class name 
is general. My yellow dog, the honesty of Lincoln, Albert 
White, New York City, are individual notions, while dog, 
honesty, man, city, are general notions. 

A sure way to determine whether the notion is indi- 
vidual or general is to attempt to divide it into its kinds. 
Only general notions may be subdivided. 

5. KNOWLEDGE AND IDEA AS RELATED TO THE 
NOTION. 

Knowledge is anything known, while anything of which 
the mind becomes aware is a notion. Notions are always 
bits of knowledge, but knowledge is not always a notion. 
Notions are mental products belonging to the mind which 
thinks them, while knowledge, though it must first be a 
mental product of someone's mind, may not necessarily 
be a product of yours or mine. Notions are always found 
in the mind, while knowledge may be found in books, but 
not necessarily in some individual mind. Knowledge 
stands for everything knoivn, the notion, for everything 
noted. The Egyptians may have possessed much knowl- 
edge of which we may never become aware. Much of 
their knozvledge may never become notions of the Ameri- 
can people. A notion is an existing state of consciousness. 
Said notion may be committed to paper, and then it may 
give way to another notion. It now ceases to be your no- 



1 6 Thought and Its Operation 

tion, but remains on the printed page, as a bit of know! 
edge. 

"Idea," because of its ambiguity, really has no place in 
logic. The term is frequently restricted to a reproduced 
percept. To illustrate : When the pencil is before me the 
mental product is a percept, but when the pencil is with- 
drawn and I try to think of it, then have I an idea of 
"pencil." Probably idea is most commonly associated 
with meaning and belief. To illustrate: What is your 
idea as to the meaning of homogeny? or What are your 
ideas on the tariff? 



6. THE LOGIC OF THE PSYCHOLOGICAL TERMS IN- 
VOLVED IN THE NOTION. 

Concerning the knowing mind the psychologist classifies 
its activities and their products as follows: 






Activity 


Product 


( i ) Presentative 




(i) Sensation 


Sensation 


(2) Perception 


Percept 


(2) Representative 




(1) Imagination] 

(2) Memory ^ 


Image 


(3) Thinking 




(1) Conception 


Concept 


(2) Judging 


Judgment 


(3) Reasoning 


Inference 



The notion as any product of the knowing mind in- 
cludes the six products as indicated by the psychologist. 

The individual notion which is intuitive includes the 
sensation, percept and image ; the general notion which is 



The Logic of the Psychological Terms 



17 



Individual notion= 



intuitive products 



a thought product stands for the concept, judgment and 
inference. To put it mathematically — 

'sensation^ 

percept 

image 
r - ° ^ J Ynotion 

[ concept 

General notion=*{ judgment j>=thought products 

[inference] 

As we shall have occasion frequently to refer to these 
psychological terms it may be well to define them. 

Logical Definition. 



Psychological Definition. 

A sensation is the first 
and simplest mental result 
of the stimulation of an 
incarrying nerve. 

A percept is a mental 
product which results from 
a consciousness of particu- 
lar material things present 
to the sense. 

An image is a mental 
product which results from 
particular material things 
not present to the sense. 

A concept is a re-pres- 
entation in our minds an- 
swering to a general name. 

A judgment is the result 
of asserting an agreement 
or disagreement between 
two ideas. 



A sensation is a vague, 
unlocalized mental product 
of the knowing mind. 

A percept is a consciously 
localized group of sensa- 
tions. 



An image is a reproduced 
percept. 



A concept is a mental 
product arising from think- 
ing many notions into one 
class. 

A judgment is the mental 
product arising from con- 
joining or disjoining no- 
tions. 



1 8 Thought and Its Operation 

Psychological Definitions— Con. Logical Definitions— Con. 

An inference is a judg- An inference is a judg- I 
ment derived from per- ment derived from ante- f 
ceiving relations between cedent judgments, 
other judgments. 

It is seen that the sensations furnish the raw material. 
Ignoring the few exceptions we may then say that a per- 
cept is a made-over group of sensations; a concept a 
thought-made group of percepts; a judgment a thought- 
made group of concepts; an inference a judgment derived 
from other judgments. 

Developed thinking is first found in the concept, and as 
we study the thought products, "concept," "judgment" 
and "inference," the truth is forced upon us that thinking 
as a process aims to group the many into one. From 
many percepts is built the one concept, from two concepts 
is built the one judgment and from two judgments is 
built the one inference.* 

Speaking figuratively, thinking is a matter of picking 
up the fragments along the shore of consciousness and 
tying them into bundles. 
7. Thought in the Sensation and Percept. 

So far in this discussion it has been assumed that there is 
no thinking involved in the sensation or the percept. There 
are good authorities, however, who insist on dignifying the 
sensation, even with a crude form of thinking. To illustrate: 
One may be reading an interesting novel. The mind is being 
entertained and ignores the activities of the objective world, 
yet we cannot say that the mind is dead to the world outside. 
There is a dim consciousness of certain noises without. These 
unlocalized sounds are sensations; but how is the mind able to 
recognize them as sounds or noises? To interpret the noises is 



Mediate Inference. 



The Logic of the Psychological Terms 19 

it not necessary for the mind to affirm a connection between them 
and some past mental experience? Is it possible for the mind 
to know anything without establishing some kind of connection 
between the outside occurrence and an inner situation? If this 
is granted then in sensation there must be implicit thinking. 

As the percept is a localized group of sensations then there 
must be involved in perception a more complex form of think- 
ing, since in grouping sensations there is a recognition of 
connections. 

If there is thinking in the sensation which is the simplest 
and lowest form of the knowing-mind then thinking conditions 
all knowledge and really is the basic elemental cell of all 
knowing. 

On the other hand there are those who maintain that the 
sensation and percept are mere reflections of consciousness; 
the sensation being a reflected quality and the percept a 
reflected object. These mental situations come into being in- 
stantly — there is no time for thought and we all know that 
thought requires time. ("As quick as thought" is misleading, 
since light travels more rapidly by many times than the agencies 
of thought.) 

It will probably never be settled to the satisfaction of all just 
when thinking commences. The question is as difficult as some 
others which have never been solved. For example: Where 
does life commence? When does the plant merge into the ani- 
mal? Which was first the egg or the hen? Does the ob- 
jective world really exist or is it only a mental interpretation 
of vibrations? etc. 

Logically considered the question is immaterial. All will 
agree that developed thought is involved in the concept, judg- 
ment and inference, while, if it appears at all in the percept 
and sensation, it is more or less undeveloped and consequently 
lies quite without the province of the logical field. 

8. EVOLUTION AND THE THINKING MIND. 

Speaking in general terms evolution is a development 
from a lower to a higher state. Thus have come the 
various species of the vegetable and animal world. The 



20 Thought and Its Operation 

lower orders of life are simple in structure and func- 
tion. In the one-celled animate form a single organ 
performs all of the work needed to maintain life and 
perpetuate the species. If these simple life- forms are 
cut in two, life continues in the two parts as if nothing 
had happened. Aside from their simplicity there is little 
of interdependence of function and little of co-ordina- 
tion of organs in the lowest life-forms. In short there 
is no division of labor ; "each cell is a world unto itself." 
An analogous development is seen in the thinking 
mind. The little child thinks in lumps, and these lumps 
are only faultily linked together, but the adult thinks in 
terms of the grains of the lump, each grain having its 
place, which it must occupy for the sake of all the other 
grains as well as the entire lump. The child's thinking 
is vague, general and inaccurate, while the adult's think- 
ing should be definite, specialized and accurate. Think- 
ing in the lump means little discrimination and very 
faulty integration or unity, while thinking in terms of 
the grains means detailed discrimination and perfect 
integration. To illustrate : The child sees a dog trotting 
along the side walk which, according to the suggestion of 
his mother, he learns to call "bow-wow." Later he ob- 
serves a cat and at once says "bow-wow," because all that 
the child notes is that something with legs, ears and a tail 
is trotting along the side walk. Anything which fits these 
general marks is a "bow-wow." Similarly when a child 
first observes a robin perched on a gate post he fails to 
distinguish between the two — it is all bird from the top of 
the robin's head to the bottom of the gate post. 



The Logic of the Psychological Terms 21 

Progress in thinking is measured by progress in dis- 
crimination. The skilled thinker divides the large unit 
into very small units, compares these with each other 
and then reunites them into a more perfect and unified 
whole. First there is an analysis and then a synthesis. 
Like a shuttle the power of thought works in and out; 
it goes in to separate, it comes out to unify. 

There is another aspect in the analogy between the 
life of the physical and mental worlds. Somewhere in 
the order of progress there is a connecting link between 
the mineral and vegetable kingdoms, likewise between 
the vegetable and animal kingdoms. The sensation is 
as much a state of feeling as an act of knowing and 
consequently is the connecting link between the feeling 
mind and the knowing mind. If the percept is the re- 
sult of thinking as well as intuition then it may stand for 
the dividing line between the knowing* mind and the 
thinking mind. 

9. The Concept as a Thought Product. 

Conception is the process of thinking many notions into one 
class. The product of such a process is called a concept. (1) 
The concept may stand for a group of concrete general notions 
— as the concept man, which stands for the five general notions : 
Caucasian, Mongolian, Ethiopian, Malay and American Indian. 
(2) The concept may stand for a group of concrete individual 
notions. For example, the same concept man represents all of 
the individual men of the world. (3) The concept may stand 
for a group of abstract general notions. To wit: Virtue rep- 
resents such general notions as honesty, justice, industry, 
purity, etc. (These are general notions because they admit of 
a subdivision into kinds. Industry, for instance, may be di- 



* Intuitive Knowing. 



22 Thought and Its Operation 

vided into two kinds: mental industry and physical industry.) j 
(4) The concept may stand for a group of abstract individual 
notions. To illustrate: Blueness stands for the various shades ! 
of blue, as sky blue, bird's egg blue, navy blue, etc. 

Thus does the concept stand for a group of all kinds of ; 
notions, individual and general, abstract and concrete. 

The Process of Conception Illustrated. 

I see for the first time in my life a pencil. In other words j 
I become conscious of a localized group of sensations — this i 
is a percept. I am told that the name of that which I see is I 
pencil. I note that this particular pencil has a thread of black j: 
lead encased in a cylindrical strip of wood which is brown in 
color. A second object is presented which I recognize as a ! 
pencil though the shape is prismatic rather than cylindrical 
and the color green rather than brown. But I call it a pencil ij 
because it has a thread of black lead encased in a strip of 
wood. The notion which I now have in mind stands for two 
pencils and is therefore represented by a class name. As I 
observe other pencils of various shapes, made of wood and 
paper with threads of different colored lead, my notion of 
pencil broadens till finally it stands for all pencils. This is the r. 
process of conception according to the definition, namely: "The j 
process of thinking many notions into one class." In this case I. 
the notions are individual. 

An examination of conception makes evident two distinct charac- ': 
teristics. First, I may be able to recignize each individual pencil be- ji 
cause of the two common qualities, a thread of lead and an encase- |i 
ment of some kind. This process of the knowing mind whereby it j. 
recognizes and affirms connections is called thinking as we have al- 
ready learned. Here is the thinking aspect of conception. Second, as | 
the instances of the observed objects are multiplied, my notion of r, 
pencil is broadened. It is a building process where many are cemented ' 
into one ; like the blocks of a cement wall. Here we find the charac- - 
teristic which enables us to call the process conception. This is the f 
mark which distinguishes conception from all the other thought ! 
processes. 

10. The Judgment as a Thought Product. 
Judging is the process of conjoining and disjoining notions, j 






The Logic of the Psychological Terms 23 

The product of judging is the judgment and all judgments are 
expressed by means of propositions. A proposition consists of 
one subject and one predicate connected by some form of the 
verb be or its equivalent. 

(1) A judgment may conjoin or disjoin two individual notions. 
To wit: Conjoined — This pencil belongs to Albert White. 
Disjoined — This pencil does not belong to Mary Smith. 

(2) A judgment may conjoin or disjoin two general notions. 
Conjoined — Some men are virtuous. 

Disjoined — Some men are not virtuous. 

(3) A judgment may conjoin or disjoin a general and an 
individual notion. 

Conjoined — Abraham Lincoln was virtuous. 

Disjoined — Edgar Allen Poe was not temperate. 

In order that the knowing mind may conjoin notions it must 
recognize some mark of similarity or connection. This is the 
thinking aspect of the judgment. It is likewise to a certain 
degree the judging aspect as the latter is simply a matter of 
affirming or denying connections between notions. But think- 
ing is a broader term than judging. There may be connections 
established between a name and a notion. For example in the 
case of the dog which the child sees trotting along the side- 
walk and which the mother refers to as a "bow-wow"; the 
term "bow-wow" is not a percept and has no meaning inde- 
pendent of its association with the dog, hence it is not a no- 
tion, yet some connection has been made in the child's mind 
between "bow-wow" and his notion of dog. This is a simple 
form of thinking, but not of judging, as the latter affirms or 
denies connections between notions only. 

The fact that judging and thinking so closely resemble each 
other has given just cause for some logicians to designate 
judging as the most fundamental element in all thinking. 
"The simplest form of thinking," says Creighton, "is judging." 
In order to think many notions into one class it is necessary 
to conjoin notions. To illustrate: The child who has a general 
notion of man sees for the first time a negro. If he recognizes 
the negro as a colored man he must conjoin his general notion 
of man with this individual notion. In short, a concept is built 
by means of a series of judgments. It may be said further 



24 Thought and Its Operation 

that an inference is simply a made-over judgment. It is thus 
evident that judging appears in both the thought processes of 
conception and inference and, therefore, as a final conclusion 
it may be affirmed that judging, though perhaps not the sim- 
plest form of thinking, is the basic element of developed thought. 

11. Inference as a Thought Product. 

Reasoning is the process of deriving a new judgment from a 
consideration of other judgments. The product of any reason- 
ing process may be called an inference, although, as will appear 
in a later chapter, inference is commonly used as indicating 
the process as well as the product. 

Often reasoning may assume a syllogistic form with the in- 
ference as its conclusion. A syllogism is an arrangement of 
three propositions using three different terms. The following 
are syllogisms : 

(1) All children should play. 

Mary is a child. 

Hence, Mary should play. 

(2) No teacher should judge hastily. 

You are a teacher. 

Hence, you should not judge hastily. 
In the second syllogism the inference, "you should not judge 
hastily," is derived from the other two judgments by merely 
eliminating the common term teacher and disjoining the re- 
maining two terms. The inference is consequently a new judg- 
ment. Therefore, reasoning is only a matter of judging carried 
to a more complex stage. 

To summarize — conception is largely a matter of conjoining 
a general notion with an individual notion, judging of conjoin- 
ing and disjoining all kinds of notions and inference of con- 
joining and disjoining judgments. All three processes go to 
form the larger process of thinking. The concept, the judg- 
ment and the inference are products arising from conjoining 
and disjoining notions. 

12. THINKING AND APPREHENSION. 

Says Jevons: "Simple apprehension is the act of the 
mind by which we merely become aware of something, 



Thinking and Apprehension 25 

or have an idea or impression of it brought into the 
mind;" while Hyslop states that "The process of 
knowledge which gives us percepts is apprehension." 
It is obvious that the idea of the latter is that appre- 
hension yields individual notions only, while Jevons, in 
citing the term iron as an illustration of his definition, 
would infer that the general notion is the product of 
apprehension. The term is strikingly ambiguous and 
will not be referred to often in this treatise. If the stu- 
dent desires a definition this will cover the concensus of 
opinion on the meaning of apprehension. Apprehension 
is that process of the knowing mind which yields the 
percept and concept. Some logicians give to the think- 
ing mind the three aspects of apprehension, judging and 
reasoning. 

13. STAGES IN THINKING. 

In all thinking there are three steps or stages which 
may be termed discrimination, comparison, integration. 

In the case of the two pencils held in the hand, it is 
noted that one is longer than the other. Let us analyze 
the process which made possible this conclusion. Step 
one — Attention is given first to one pencil and then to 
the other. In each case the pencils are distinguished 
from the hand and the other surrounding objects. This 
is discrimination. Step two — The pencils are compared 
in length. Step three — The two notions are united in 
the judgment, "Pencil number one is longer than pencil 
number two." This is integration. 

Another illustration. The child is requested to solve 



26 Thought and Its Operation 

this problem : If 8 tons of hay cost $165, what will 16 
tons cost? 

Statement: Given: 8 tons cost $165 
Required: 16 tons cost ? 

Discrimination. The child notes that 8 tons cost $165 
and at this rate he is required to find the cost of 16 tons. 

Comparison. The child perceives that 16 tons is twice 
8 tons. 

Integration. The child concludes that the cost of 16 
tons will be twice the cost of 8 tons or $330. 

When we think, we first tear to pieces that we may 
become acquainted with every part. This may be called 
analysis. Then we put the related pieces together again. 
This may be called synthesis. Before, however, the 
parts are re-united a certain amount of comparison is 
necessary. The three stages of thought might thus 
be denominated: (1) analysis, (2) comparison, (3) 
synthesis. 

After the synthesis or integration it is necessary to 
name the result, consequently a fourth step is sometimes 
given, namely denomination. 

14. OUTLINE. 

Thought and Its Operation. 

(1) The Knowing Mind Compared with the Thinking Mind. 

(2) Knowing by Intuition. 

(3) The Thinking Process. 

Denned. 

Other definitions. 

(4) Notions. 

Individual. 

General. 

Thing and object distinguished. 



Outline 27 

(5) Knowledge and Idea as Related to the Notion. 

(6) The Logic of Psychological Terms Involved in the 

Notion. 

The sensation "1 

The percept Llndividual notions. 

The image 

The concept "] 

The judgment LGeneral notions. 

The inference 

Terms defined. 

(7) Thought and the Sensation and Percept. 

(8) Evolution and the Thinking Mind. 

(9) The Concept as a Thought Product. 

(10) The Judgment as a Thought Product. 

The simplest form of thinking. 

(11) Inference as a Thought Product. 

(12) Thinking and Apprehension. 

(13) Stages in Thinking. 

Discrimination. 
Comparison. 
Integration. 
(Denomination.) 

15. SUMMARY. 

(1) Knowing is a broader term than thinking as the former 
equals the latter plus intuition. 

(2) Intuitive knowledge is that which comes to the mind im- 
mediately by direct observation. 

Although intuitive knowledge comes to the mind without 
thought, yet such knowledge is essential to all thinking. Intuitive 
knowledge is the foundation upon which the thinking mind builds. 

(3) Thinking is the deliberative process of affirming and 
denying connections. Thinking is a "thickening process," the 
smaller units being pressed together to make a larger. Thinking 
is chiefly a matter of reducing plurality to unity. 

(4) A notion is any product of the knowing mind. 
An individual notion is the notion of one thing. 

A general notion is a notion of a class of things. 



28 Thought and Its Operation 

A thing includes objects, qualities, relations or any existing 
entity. A thing is that which has individual existence. 

(5) A bit of knowledge must have been a notion of some one's 
mind, but may not necessarily be a notion of your mind. Knowl- 
edge may be found in books, but a notion is a mental product 
found only in the mind. Idea is ambiguous, though its meaning 
is usually restricted to an image, a meaning or a belief. 

(6) The products of the knowing mind are the sensation, the 
image, percept, concept, judgment, inference. 

The sensation, image and percept are individual notions, while 
the concept, judgment and inference are general notions. 

A sensation is a vague, unlocalized product of the knowing 
mind. 

A percept is a consciously localized group of sensations. 

An image is a reproduced percept. 

A concept is a mental product arising from thinking many 
notions into one class. 

A judgment is a mental product arising from conjoining and 
disjoining notions. 

An inference is a judgment derived from antecedent judgments. 

The developed thought processes are the concept, the. judgment 
and the inference. 

(7) Just where the simplest form of thinking appears in the 
various activities of the knowing mind is still an undecided ques- 
tion. It is agreed that thinking in its developed and more com- 
plex form is found in conception, judging and reasoning. 

(8) Thinking evolves from the simple to the more complex, 
just as life has evolved. 

The child thinks in vague, indefinite wholes, while the adult 
thinks in clear, definite parts. The child discriminates very 
imperfectly while the adult discriminates accurately. 

The sensation seems to be the connecting link between the feel- 
ing mind and the knowing mind, while the percept links together 
the knowing mind and the thinking mind. 

(9) Conception is the process of thinking many notions into 
one class. The product of such a process is a concept. The con- 
cept stands for groups of all kinds of objects. 

Conception has the two aspects of affirming connections and of 
building many into one. The first is the thinking side of the 



Outline 29 

process and the second is the mark which distinguishes concep- 
tion from the other thought processes. 

(10) Judging is the process of conjoining or disjoining notions. 
Judgment is the product of judging. 

Judgments conjoin and disjoin all kinds of notions. 

Judging and thinking, though they closely resemble each other, 
are not synonomous terms. Thinking is a broader term in that 
connections may be established between a notion and a name for 
that notion. 

Judging is the most fundamental of all thinking, as the concept 
is built from a series of judgments and an inference is simply a 
made-over judgment. 

(11) Inference. 

Reasoning is the process of deriving a new judgment from a 
consideration of antecedent judgments. This derived judgment 
may be called an inference. Sometimes the term inference de- 
notes the process of reasoning as well as the product. 

Reasoning often takes the form of a syllogism. 

The concept, the judgment and the inference are products 
arising from conjoining and disjoining notions. 

(12) Some give to the thinking mind the three aspects, appre- 
hension, judging and reasoning. Apprehension is another word 
for the two processes, perception and conception. 

(13) The three important stages in thinking are discrimination, 
comparison, integration; or analysis, comparison and synthesis. 

16. REVIEW QUESTIONS. 

(1) Show the difference between the knowing mind and the 
thinking mind. 

(2) Describe the process known as intuition. 

(3) What is intuitive knowledge? 

(4) Is the assumption that think comes from the same root as 
thick a feasible one? Explain. 

(5) Define thinking in at least two ways. 

(6) "Inability to think is due to inability to note connections." 
Show this by making use of some problem in arithmetic. 

(7) Distinguish between individual and general notions. 

(8) Which is the broader term, object or thing? Explain. 



30 Thought and Its Operation 

(9) What kind of notions only admit of subdivisions? Illus- 
trate. 

(10) What is the difference between knowledge and notions? 
Explain. 

(11) Explain and illustrate the meaning of idea. 

(12) Classify the various activities of the knowing mind and 
define each. 

(13) Explain by definition and illustration the products of the 
knowing mind. 

(14) Relate the general notion to the psychological products of 
the knowing mind. 

(15) "The thinking mind is a unit." Explain fully. 

(16) Trace the analogy between the evolution of the physical 
world and the evolution of thought. 

(17) Show that the sensation and the percept may be regarded 
as connecting links between lower and higher states. 

(18) Define and illustrate conception. 

(19) Show that the concept stands for all kinds of notions. 

(20) Point out the thinking aspect of conception as distin- 
guished from the activity which gives the process its name. 

(21) Define the judgment. Illustrate two kinds. 

(22) Show that the concept is built by means of a series of 
judgments. 

(23) Show that judging is the fundamental element in the 
thought products. 

(24) Define and illustrate reasoning. 

(25) Describe the syllogism. 

(26) Explain the use of apprehension. 

(27) What are the stages in thinking? Illustrate fully. 

(28) Show that thinking is a matter of analysis and synthesis. 

17. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Give your argument in favor of the statement, "Dogs 
think, but do not reason." 

(2) Show by illustration that thinking would be impossible 
without intuition. 

(3) "Thinking is the conscious adjustment of a means to an 
end in problematic situations." Illustrate this. 






Questions for Original Thought and Investigation 31 

(4) The class is unable to solve the following problem: "I 
sell my house for $12,000, which is a gain of 25% on the cost. 
Find the cost." What is the trouble? State the problem so that 
some connection is apparent. 

(5) "Two-thirds of my salary is $2,400. What is my sal- 
ary?" A child solves this by dividing $2,400 by two and multiply- 
ing this result by three. Illustrate a plan for establishing right 
connections. 

(6) May a judgment express a general notion? Illustrate. 

(7) Is a thought a thing? Illustrate. 

(8) Show the illogic of dividing notions into individual, 
general and abstract. 

(9) Show that goodness is a general notion. 

(10) Is the concept an idea? Explain. 

(11) Prove that a mental image is always an individual notion. 

(12) "In sensation is there implicit thinking?" Argue both 
sides of the question. 

(13) Show that the concept, the judgment and the inference 
are products of the thinking mind. 

(14) Show by illustration where perception ceases and concep- 
tion begins. 

(15) Is there actually any difference between thinking and 
judging? Illustrate. 

(16) "Reasoning is controlled thought." Explain. 

(17) Of the three stages in thinking which one most concerns 
the teacher? Illustrate. 



CHAPTER 3. 

THE PRIMARY LAWS OF THOUGHT. 

1. TWO FUNDAMENTAL LAWS. 

The elemental form of evolved thought is the judg- 
ment. The laws or axioms of thought may, therefore, 
be discovered by studying the judgment. 

Judging is the process of conjoining and disjoining 
notions. When these notions are conjoined the judg- 
ment is affirmative; when disjoined the judgment is 
negative. To illustrate: "Some men are wise," is an 
affirmative judgment, while "Some men are not wise," is 
a negative judgment. All judgments are either affirma- 
tive or negative and this suggests that there may be but 
two fundamental laws or axioms underlying judging or 
all forms of developed thinking. One law would condi- 
tion the affirmative judgment; the other the negative. 
Such is actually the case. The law which permits the 
affirmative judgment is called the law of identity, while 
the law which allows a negative judgment is known as 
the law of contradiction. There is a third law termed 
the law of excluded middle, which is in reality a com- 
bination of the other two. 

2. THE LAW OF IDENTITY. 

In general the law of identity implies a certain perma- 
nency throughout the material world. That door is a 
door and always will be a door till the conditions 
change. If it were not for this law, that everything is 

32 



The Law of Identity 33 

permanently identical with itself, it would be impossible 
to think at all. For example: Take away the notion of 
permanency from the door and thought becomes at once 
ridiculous. Suppose that while we are asserting that 
the object is a door, it changes to a tree, and while we 
insist that the object is now a tree, it changes to a cow, 
etc. We can readily see that it would hardly be worth 
while to think at all. 

The law of identity may be stated in three ways :• ( 1 ) 
Whatever is, is; (2) Everything remains identical with 
itself; (3) The same is the same. 
Absolute Identity — Complete and Incomplete. 

Applying the law of identity to the affirmative judg- 
ment expressed in the form of a proposition, we find two 
kinds of identity, absolute and relative. In the proposi- 
tions, "Socrates is Socrates," "dogs are dogs," "honesty is 
honesty," the subject is absolutely identical with the predi- 
cate — the same in form and meaning. If we were to 
illustrate the subject and predicate by two circles they 
would be of the same size and shape, the one coinciding 
with the other point to point. 

This kind of absolute identity which makes possible 
all truisms we may term, for want of a better name, 
complete absolute identity. This would imply that there 
is an incomplete absolute identity and such seems to be 
the case. Examining the definition, "A man is a rational 
animal," we observe that the notion man has the same 
content or meaning as the notion rational animal. In 
meaning, then, the two notions are absolutely identical. 
The one includes just as many objects or qualities as 



34 The Primary Laws of Thought 

the other, and if we were to draw two circles repre- 
senting them, they would be of the same size. In form, 
in mode of expression, however, the notions differ and 
the circles, though coinciding, would need to differ in 
form, the boundary of one might be a solid line, the other 
a dotted. This we may call incomplete absolute identity. 
All logical definitions illustrate identities of this kind. 

Relative Identity. 

Relative identity is best understood by thinking of it 
as partial identity, just as we may think of absolute iden- 
tity as total identity. In relative identity the whole of 
one notion may be affirmed of a part of another notion; 
or a part of one notion may be affirmed of a part of 
another notion. To illustrate: (i) All men are mortal; 
(2) Some men are wise. These and their like are made 
possible because of the law of relative identity. In the first 
proposition all of the "men" class is identical with a part 
of the "mortar class. If we were to represent this rela- 
tion by circles, the "men" circle would be made smaller 
than the "mortal" circle and placed inside it, as in Fig. 1. 

Mortal 

[yen J 

Fig. 1. Fig. 2. 

Be it remembered that circles are surfaces, and in Fig. 
1 the men circle is identical with that portion of the 
mortal circle which is immediately underneath it. 




The Law of Identity 35 

The same relation may be indicated by a small pad being 
placed on top of a larger pad. Then the whole of the smaller 
pad could be thought of as being identical with that part 
of the larger pad which is immediately underneath. 

In the case of the second proposition a part of the 
"men" class is identical with a portion of the "wise" 
class. The two circles indicating this relation must inter- 
sect each other so that a portion of each may be common 
ground, as in Fig. 2 where the shaded part represents 
the identity. 

Thus we see that the law of identity underlies all 
affirmative propositions. Absolute identity making pos- 
sible the truism and definition, and relative identity con- 
ditioning all the universal and particular affirmative 
propositions which are neither truisms nor definitions. 

The three forms may be symbolized as follows : 

(1) A is A — Absolute complete 

(2) A is A — Absolute incomplete 

(3) A is B— Relative. 

The student will note that the "A's" of absolute in- 
complete differ in form. 

3. LAW OF CONTRADICTION. 

The law of contradiction underlies all negative propo- 
sitions. It is the mission of this law to tear down or to 
be destructive in nature ; while the law of identity builds 
up or is constructive in nature. 

The law of contradiction may be stated in this way: 
It is impossible for the same thing to be and not to 
be at the same time and in the same place. Or better, it 



36 The Primary Laws of Thought 

is impossible for the same thing to be itself and its con- 
tradictory at the same time. Bringing out a further 
aspect, no thing can have and not have the same attri- 
butes at the same time. 

The little word not bisects the universe. All the peo- 
ple in the world are either honest or not honest, virtuous 
or not virtuous. These are contradictory statements and j 
what is comprehended by the one cannot be comprehended 
by the other at the same time, any more than a man can 
shake his head and nod his head at the same time. 

If we assert the identity between two notions then we 
cannot in the same breath deny their identity. 

Illustrations : 

(1) A red flower cannot be a red flower and not a 
red flower at the same time. 

(2) No man can be guilty and not guilty at the same 
time. 

(3) A boy cannot be working and not working at the 
same time. 

If I assert that the flower is red, then I cannot affirr 
in the same breath that the flower is not red. 

Two Uses of Not. 

The word not when used with the copula of a given 
proposition makes that proposition negative;, as (1) "Some 
men are not wise." But when not is attached to the 
predicate by a hyphen, the predicate is made negative, 
not the proposition, as (2) "Some men are not-wise." 
Here the predicate not-wise is negative, but the proposi- 
tion in which it appears is affirmative. It is obvious that 



The Law of Contradiction 37 

the proposition "Some men are not wise" illustrates the 
law of contradiction, since the some men referred to 
are contradicted of all which is wise. Whereas the 
proposition "Some men are not-wise" illustrates relative 
identity, since the subject "some men" is affirmed of a 
part of the predicate "not-wise." The student may be 
led to see these relations by drawing circles, the one to 
represent the subject, the other the predicate. (See page 
141.) 

Further Illustrations : 

Some teachers are wise *] 

Some teachers are not-wise llllustrate the law of 

Some teachers are unwise j identity. 

Some teachers are not wise 1 

■ 

Some teachers are not not-wise llllustrate the law 
Some teachers are not unwise. j of contradiction. 

The student must understand that a term and its con- 
tradictory destroy each other. If we affirm something 
of the one, then we must deny it of the other, or we 
undermine the integrity of both. If it is affirmed of 
teachers A, B and C that they are wise, then it must 
be denied that they are not-wise. 

Illustrations : 

A, B and C are wise "1 These are mutually de- 
A, B and C are not-wise j structive. 

A, B and C are wise. 1 These are not mutually de- 
A, B and C are not not- I structive, but virtually 
wise. j mean the same thing. 



38 The Primary Laws of Thought 

Symbolization of the Law of Contradiction. 

A is not not-A. A is not B. 

(As A is always A it or or 

would be absurd to say A is not not-B. 

that A is not A.) 

Contradictory and Opposite Terms. 

It is easy to use opposite terms in a contradictory 
sense. This leads to serious error. "Not-guilty" is the 
contradictory of "guilty," while "innocent" is the opposite 
of "guilty." We could hardly say that the water must 
either be cold or hot, as it might be warm. "Not-hot" is 
the only term which contradicts "hot." The law of 
contradiction has nothing to do with opposites. 

Further, it is dangerous to regard words with the nega- 
tive prefix as being contradictory of the affirmative 
form. For example: Valuable and invaluable are not 
contradictory. There is likewise some doubt as to the 
contradictory nature of such words as agreeable and dis- 
agreeable, though we are sure that agreeable and not- 
agreeable contradict each other. To use the "not" with a 
hyphen is safer than to depend upon some prefix which 
is supposed to mean "not." 

Illustrations of Contradictory and Opposite Terms. 



c 


pposite. 

A 


Contradictory. 

A 


bad 


good 


bad 


not-bad 


soft 


hard 


soft 


not-soft 


cold 


hot 


cold 


not-cold 


rough 


smooth 


rough 


not-rough 



The Law of Excluded Middle 39 

Opposite — Continued Contradictory — Continued 



r 

good 


evil 


t 

good 


> 

not-good 


warm 


cool 


warm 


not- warm 


weak 


strong 


weak 


not-weak 



4. THE LAW OF EXCLUDED MIDDLE. 

The law of excluded middle may be considered as a 
combination of identity and contradiction. Identity 
gives the proposition, "John Doe is honest." Contradiction, 
"John Doe is not honest." Combine the two using either 
and or and we have the excluded middle proposition, 
"Either John Doe is honest or he is not honest." 

Excluded middle explains itself. Of the two contra- 
dictory notions it must be either the one or the other. 
There is no "go-between" notion. 

The law may be stated in many ways, as will be seen 
by the following : ( 1 ) Everything must either be or not 
be. (2) Either a given judgment is true or its contra- 
dictory is true; there is no middle ground. (3) Of two 
contradictory judgments one must be true. (4) Every 
predicate may be affirmed or denied of every subject. 

Illustrations : 

(1) A man is either mortal or he is not mortal. (2) 
John Doe is either honest or not-honest. (3) Either 
you are going or you are not going. 
Symbolization of Excluded Middle. 
A is either A or not-A 

or 
A is either B or not-B. 



40 



The Primary Laws of Thought 



5. THE LAW OF SUFFICIENT REASON. 

The law may be stated in this wise. Every phenome- 
non, event or relation must have a sufficient reason for 
being what it is. To illustrate : (i) If Venus is the even- 
ing star, there must be a sufficient reason. (2) If thfc 
ground is wet, there must be a cause. Many logicians 
argue that this law has no place in logic, its field being 
that of the physical sciences. The laws of identity, con- 
tradiction and excluded middle are, however, universally 
regarded as the Primary Laws of thought. 



6. UNITY OF PRIMARY LAWS OF THOUGHT ILLUS- 
TRATED BY SYMBOLS. 



(1) Absolute Symbols 



Relative Symbols. 



Excluded middle. 
A is either A or not-A. A is either B or not-B. 



Contradiction. 
A is not not-A. 

Identity. 
A is A. 



A is not B or A is not not-B. 



A is not-B or A is B. 
(2) Propositions made to fit symbols. 

Excluded middle. 

A man is either a man A man is either honest or 
or a not-man. not-honest. 

Contradiction. 
A man is not a not-man. A man is not honest, or a 

man is not not-honest. 



Unity of Primary Laws of Thought 41 

Identity. 

A man is a man. A man is not-honest, or a 

man is honest. 

The "excluded middle" propositions of the foregoing ex- 
press alternatives which are mutually contradictory. 
There is no middle ground. The "contradictory propo- 
sitions" contradict the identity of the subject with one 
alternative, while the "identity" propositions affirm the 
identity of the subject with the other alternative. This 
is made possible because of the principle, "Of two 
mutually contradictory terms, if one is true the other 
must be false." The foregoing scheme shows how 
closely "contradictory" and "identity" propositions are 
related to "excluded middle" propositions. Expressed 
mathematically: excluded middle = contradiction + 
identity. 

7. OUTLINE. 

Primary Laws of Thought. 

(1) Two fundamental laws. 

Identity, contradiction. 

(2) Law of identity. 

Absolute — complete, incomplete. 
Relative. 

(3) Law of contradiction. 

Two uses of not. 

Contradictory and opposite terms. 

(4) Law of excluded middle. 

(5) Law of sufficient reason. 

(6) Unity of primary laws of thought. 



42 The Primary Laws of Thought 

8. SUMMARY. 

(1) The elemental forms of evolved thought are the affirm- 
ative and negative judgments. This suggests two fundamental 
laws of thought, the law of identity and the law of contradic- 
tion. The former conditions the affirmative judgment, the latter 
the negative. 

(2) The law of identity implies a permanency of being. 
"Everything remains identical with itself," is a statement of 
identity. 

Absolute identity may be divided into complete and incomplete 
identity. 

In complete absolute identity the subject is the same as the 
predicate in both form and meaning. Truisms illustrate this. 

In incomplete absolute identity the subject is identical with 
the predicate in meaning only. Illustrated by definitions. 

In relative identity the whole of the subject may be affirmed 
of a part of the predicate or a part of the subject may be 
affirmed of a part of the predicate. 

(3) "It is impossible for the same thing to be itself and its 
contradictory at the same time," is a statement of the law of 
contradiction. Identity is constructive while contradiction is 
destructive in nature. To make the proposition negative the 
word not must be used with the copula. "Not" attached to the 
predicate with a hyphen makes the predicate negative, but not 
the proposition. 

To use opposite terms in a contradictory sense leads to serious 
error. 

The safest way of making a positive term a contradictory 
negative term is to prefix "not" with a hyphen or use "non." 

(4) The law of excluded middle is virtually a combination 
of identity and contradiction. It may be stated as follows: "A 
thing must either be itself or its contradictory." 

(5) "Every condition must have a sufficient reason for its 
existence," is the law of sufficient reason. Its distinct province 
is physical science rather than logic. 

(6) The laws may be expressed mathematically: excluded 
middle = identity -j- contradiction. 



Summary 

Schematic Statement of Primary Laws. 



43 



Name 


Stated 


Symbolized 


Illustrated 


Absolute identity 


Whatever is, is 


A is A 


Work is work 


Relative identity 


The whole is identical 


All A is B 


Work is a blessing 




with a part or a part is 


Some A is B 


Some play is a blessing 




identical with a part 






Contradiction 


Nothing: can both be 


A is not not-A 


Work is not not-work 




and not be at the same 


or 






time 


A is not B 


John is not honest 






A is not not-B 


Albert is not not-honest 


Excluded middle 


Everything must either 


A is either A 


Fair play is either fair 




be or not be 


or not-A 


play or not-fair play 






A is either B 


This man is either edu- 






or not-B 


cated or not-educated 



9. ILLUSTRATIVE EXERCISES. 

(la) Each of the following propositions is made possible 
because of the existence of which law of thought? 

In answering this question I summarize in my mind the mean- 
ing of each law of thought. Viz. : 

(1) In complete absolute identity the subject and predi- 

cate are the same in form and meaning. 

(2) In incomplete absolute identity the subject and predi- 

cate are the same in meaning, but not in form. 

(3) In relative identity either the whole or a part of the 

subject is identical with a part of the predicate. 

(4) The law of contradiction always denies the identity 

between subject and predicate. 

(5) Excluded middle conditions all alternative expres- 

sions. 
The Propositions. 

(1) "A thief is a thief." Complete absolute identity. 

(2) "Thinking is the process of affirming or denying 

connections." Incomplete absolute identity. 



44 The Primary Laws of Thought 

(3) "All good men are wise." Relative identity. 

(4) "No triangle has interior angles whose sum is greater 

than two right angles." Contradiction. 

(5) "A stitch in time saves nine." Relative identity. 

(6) "Judging is the process of conjoining and disjoining 

notions." Incomplete absolute identity. 

(7) "You are either a voter in this district or you are not 

a voter in this district." Excluded middle. 

(8) "Some people do not know how to live." Contradiction. 

(9) "AH is well that ends well." Incomplete absolute 

identity. 

(10) "Some men teach school." Relative identity. 

(11) "None of the planets are as large as the sun." Con- 
tradictory. 

(12) "All the trees in this grove are maple." Relative 

identity, 
(lb) Indicate the law which conditions each of the following 
propositions : 

(1) "He who laughs last laughs best." 

(2) "Perfect is perfect." 

(3) "He is a wolf in sheep's clothing." 

(4) "Either your memory is poor or you are telling a 

deliberate falsehood." 

(5) "Some of our greatest teachers thought they were 

failures." 

(6) "No man of sense would ever try to get something 

for nothing." 

(7) "Failure is not to try." 

(8) "Success is the right man in the right place doing his 

best." 

(9) "Every man is insane on some topic." 

(10) "Some pupils are not industrious." 

(11) "You are either a genius or a successful fakir." 

(12) "Honesty is the best policy." 

1C. REVIEW QUESTIONS. 

(1) How many kinds of judgments are there? Illustrate. 

(2) Name the fundamental laws of thought and explain how 
they are related to the kinds of judgments. 



Review Questions 45 

(3) Show that it would be impossible to think at all were 
it not for the law of identity. 

(4) State the law of identity in three ways. 

(5) Explain the kinds of absolute identity. Illustrate by 
propositions and by circles. 

(6) Explain by word and by diagrammatical illustration 
relative identity. 

(7) Symbolize the three forms of identity. Fit words to 
these symbols. 

(8) State in three ways the law of contradiction. 

(9) Show by illustration that not bisects the world. 

(10) Explain the uses of not. 

(11) Prove that "John Doe is not-honest," illustrates identity 
and not contradiction. 

(12) Symbolize in three ways contradiction. Fit words to 
these symbols. 

(13) Illustrate contradictory and opposite terms. 

(14) Show that words with negative prefixes are not neces- 
sarily the contradictory of the corresponding affirmative forms. 

(15) State and explain the law of excluded middle. 

(16) Symbolize the law of excluded middle. 

(17) State the law of sufficient reason. Illustrate. 

(18) Illustrate the unity of the three primary laws of thought. 

11. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Prove that the judgment is the elemental form of 
evolved thought. 

(2) What is meant by evolved thought? 

(3) Show that "Whatever is, is" is a statement of complete 
absolute identity only. 

(4) State incomplete absolute identity. 

(5) By means of one proposition state relative identity. 

(6) Show that incomplete absolute identity is a term mora 
or less illogical. 

(7) Show that these statements are exact expressions of 
relative identity : 

All men are some wise. 
Some men are some wise. 



46 The Primary Laws of Thought. 

(8) Why is the law of contradiction so named? 

(9) Show that space may be bisected by drawing a circle 
upon the black board. 

(10) Show that there is a difference in meaning between 
"You are not honest" and "You are not-honest." 

(11) Is there any difference in meaning between disagreeable 
and not agreeable? 

(12) Which is the stronger term not-just or unjust? Why? 

(13) Give a list of words in which the contradictory forms 
are expressed by the ordinary prefixes. 

(14) Illustrate by circles the law of excluded middle. 

(15) Illustrate by a line-diagram the difference between con- 
tradictory and opposite terms. 

(16) Show that the province of the law of sufficient reason 
is physical science. 



CHAPTER 4. 



LOGICAL TERMS. 



1. LOGICAL THOUGHT AND LANGUAGE INSEPARABLE. 

Any impression upon the mind tends to manifest 
itself in some form of expression. Impression which 
arouses thought tends to expression in the form of sym- 
bols. Thought and symbol go hand in hand. Expres- 
sion, taking the form of word-symbols, constitutes a 
word-language. 

It is commonly supposed that language is serviceable 
mainly in communicating one's thoughts to others, but 
language does service in another way which is quite as 
important. It tends to clarify and make definite all 
thought. Without a word-language thinking would 
lack continuity; would be vague, loose, illogical. The 
right use of a word-language, therefore, is a necessary 
adjunct to logical thought. The basic element of a 
word-language is the logical term. 

2. MEANING OF LOGICAL TERM. 

A notion has been referred to as any product of the 
knowing mind. When we express these notions in 
words such expressions may be called logical terms. 

Definition. A logical term is a word or a group of 
words denoting a definite notion. Illustrations : Honesty, 
Chicago, tree, walking, the man who was ill, beautiful 
roses. This is a list of logical terms, because each word 
or group of words denotes a notion of some kind. It is 

47 



48 Logical Terms 

now evident that any subject or predicate with its modi- 
fiers constitutes a logical term. In the proposition, "The 
beautiful red house on the hill, owned by Mr. Jones, has 
burned," the term used as the subject consists of eleven 
words. The reader must not confuse logical terms with 
grammatical parts of speech. "Of" is a preposition 
but not a logical term, as no definite notion is indicated. 

3. CATEGOREMATIC AND SYNCATEGOREMATIC WORDS. 

There are some words which, when used alone, denote 
definite notions, such as man, tree, dog, justice. On 
the other hand there are other words which, when used 
alone, do not stand for a definite notion, such as up, 
beautifully, a, and. 

Words like those in the first list are called categore- 
matic words, while those in the second list illustrate 
syncategorematic words. 

Definition. 

A categorematic word is one which forms a logical 
term unaided by other words. A syncategorematic 
word is one which must be used with other words to 
form a logical term. 

Any word or group of words which can be used as 
either subject or predicate of a proposition is a logical 
term. If the one word in question can be used as either 
subject or predicate of a proposition then it must be a 
categorematic word. If it is impossible to use the one 
word as either subject or predicate of a proposition 
then this is a sure indication that such a word is syn- 



Categorematic and Syncategorematic Terms 49 

categorematic. For example, there is no sense in the 
expressions, "And is honest," "Of is not true" ; hence and 
and of are syncategorematic. 

We may conclude from this that nouns, descriptive 
adjectives and verbs may be categorematic words, while 
adverbs, prepositions and conjunctions are syncategore- 
matic words. 

4. SINGULAR TERMS. 

A singular term is a term which denotes one object 
or one attribute. 

Proper nouns, when they stand for individuals, are 
singular terms, such as John Adams, Mississippi River, 
Socrates. Some proper names stand for a class of objects, 
as the Caesars, the Mephistopheles, the Napoleons. But 
when thus used they lose their character as proper names. 
Such names, therefore, are general terms, not singular. 

Common nouns may be made singular by some modify- 
ing word, as the first man, the pole star, the highest 
good, my pet dog, etc. 

Certain attributes which imply a oneness or a distinct 
individuality are singular, such as absolute justice, birds- 
egg blue, perfect happiness, etc. 

Some claim that terms like water, air, salt, etc., are 
singular, as they stand for one thing. This, however, 
cannot be if such terms admit the possibility of classi- 
fication as: hard water, soft water, mineral water. 

5. GENERAL TERMS. 

A general term is one which denotes an indefinite 
number of objects or attributes. 



50 Logical Terms 

Class-names are general terms, such as men, chair, 
tree, army, nation. Words like redness, sweetness, jus- 
tice, are probably general in that they denote a combi- 
nation of qualities or may be subdivided into kinds. 

The way the term is employed in the proposition 
should determine its singular or general nature. 

6. COLLECTIVE AND DISTRIBUTIVE TERMS. 

A collective term is a general term which indicates an 
indefinite number of objects as one whole. Such words 
as class, crowd, army, forest, nation, are collective. 

A distributive term is a general term which indicates 
an indefinite number of objects as a whole, and also may 
be used to refer to each one of the group separately. 
Such as man, pupil, tree, book. 

It is easy to distinguish collective from distributive 
terms when we attempt to use them in the designation 
of individuals. Pointing to a body of troops, one may 
remark, "There is the regiment." But when pointing 
to one man in the regiment, he could hardly say, "There 
is the regiment." "Regiment" is therefore collective be- 
cause it may be used with reference to the whole body 
of troops but cannot be used in connection with any 
individual of that body. On the other hand in the sen- 
tence, "Man is mortal," "man" refers to the whole family 
of men. It also indicates any one of them. As, "This 
man, John Doe, is mortal." Thus "man" is distributive. 
The distributive term, therefore, can be used in a two- 
fold sense; namely, to denote the whole or to denote 
each. 



Concrete and Abstract Terms 51 

It must be noted that, viewed from a different stand- 
point, some collective terms become distributive in na- 
ture. As for example in the proposition, "The army of 
the world is composed of able bodied men," army is used 
with reference to all armies. While it may be used to 
designate some particular army, as The American army. 

Collective terms have been classified as general terms. 
It must be borne in mind, however, that such may be 
made singular by some "modifying word. For example, 
people is a general term, but American people is a sing- 
ular term in that it refers to one people, being thus 
limited by the word American. 

7. CONCRETE AND ABSTRACT TERMS. 

A concrete term is a term which denotes a thing; e. g., 
this man, that tree, John Doe, denote in each case a 
thing. Man and tree, denote many things. All are 
concrete. 

An abstract term is a term which denotes an attribute 
of a thing; e. g., whiteness, patience, squareness, are 
abstract terms. 

Such words as red, honest, just, are concrete; while 
redness, honesty, justice, are abstract. 

On first thought it might be inferred that "red" is the 
name of an attribute just as much as "redness." This is 
a mistaken thought, however, as when we use the word 
red we mean red something — an object which is red in 
color, not the color itself. For example, in saying the 
house is red, we refer to the thing that is red, not to the 
color redness. 



52 Logical Terms 

Descriptive adjectives, because they describe things, 
are concrete. They do not alone name qualities of things, 
hence they are not abstract. 

8. CONNOTATIVE AND NON-CONNOTATIVE TERMS. 

A connotative term is one which denotes a subject and I 
at the same time implies an attribute. (A subject is any- i 
thing which possesses attributes.) 

All concrete general terms are connotative because 
they denote subjects and at the same time stand for cer- 
tain attributes ; e. g., "man" denotes many subjects ; in fact, j 
it stands for all the men in the world; it also implies ' 
rationality, the power of speech, power of locomotion, etc. 
"Triangle" stands for all plane figures of three sides; it 
likewise stands for the qualities, three-sided, three-cor- 
nered, etc. Both "man" and "triangle" are connotative. I 

A non-connotative term is one which denotes a sub- 
ject only, or implies an attribute only. Such words as j 
Boston, Columbus, The Elizabeth White, denote a sub- j 
ject only. "Blueness," "justice," "width," imply an attri- ! 
bute only. All these terms are non-connotative. The \ 
words blue, just, wide, are connotative. "Blue," for ex- j 
ample, denotes all blue things, as the blue sky, the blue ; 
sea; at the same time "blue" implies that something pos- \ 
sesses the quality, blueness. 

Generally speaking, proper and abstract nouns are 
non-connotative; though such proper nouns as Mount I 
Washington, Mississippi River, are, no doubt, connota- i 
tive, as they denote an object and imply at least one 
attribute. In the case of Mount Washington an object 



Connotative and Non-Connotative Terms 53 

is surely denoted, and the attribute mountainous is im- 
plied. Any proper noun which conveys definite infor- 
mation is connotative. It may be claimed that all proper 
nouns give information. For example, to many Boston 
indicates not only an object, but the qualities common 
to a city. In reply it may be said that "Boston" might 
indicate a boat, or a dog, or almost any individual 
object. 

9. POSITIVE AND NEGATIVE TERMS. 

A positive term is one which signifies the possession 
of certain attributes; e. g., metal, man, teacher, happy, 
honest. 

A negative term is one which signifies the absence of 
certain attributes; e. g., inorganic, unhappy, non-metallic. 

Terms which have the prefix not, non, un, in, dis, etc., 
or the affix less, are usually considered negative. The 
fact that there are some exceptions to this must not be 
overlooked. For example, unloosed, invaluable, are 
positive terms. 

In theory every positive term has its corresponding 
negative; as pure, impure; organic, inorganic; metal, 
non-metal; good, not-good. 

In some instances the language does not supply the 
word with the negative prefix because no need of it has 
been felt. The only way to express the negative of 
such words as good, table, etc., is to prefix "not" or "non." 

10. CONTRADICTORY AND OPPOSITE TERMS. 

(See page 38). 

Positive terms with their negatives have contradictory 



54 Logical Terms 

meanings and therefore are referred to as contradictory 
terms. For example, honest and not-honest, metallic 
and non-metallic, perfect and imperfect, are contradictory 
terms. Such terms are mutually destructive. When we 
assert the truth of one we also imply the falsity of the 
other. If, for example, we assert that Abraham Lincoln 
was honest, we carry with this assertion the implication 
that Lincoln was not not-honest, or that any statement 
to the effect that he was not honest is false. 

Contradictory terms, when used in a sentence, illus- 
trate the law of excluded middle, as in the statements: 
"John's recitation is either perfect or imperfect." "This 
teacher is either just or not-just." There is no middle 
ground in such propositions. 

When contradictory terms are used in classification 
the whole is divided into but two classes ; e. g. : 
honest not-honest 

agreeable not-agreeable 

metallic non-metallic 

perfect imperfect 

pure impure 

organic inorganic 

All the men in the world are either honest or not- 
honest. All the substances in existence are either or- 
ganic or inorganic, etc. 

It will also be seen from this list that the contradictory 
of the positive form is not always indicated by using the 
prefix. Honest and dishonest, or agreeable and dis- 
agreeable, are not contradictory terms. In the case of 
agreeable and disagreeable, there seems to be the middle 



Contradictory and Opposite Terms 55 

ground of absolute indifference. For example: the 
music of the orchestra is agreeable while the humming 
of the enthusiast back of me is decidedly disagreeable; 
but as to the noise upon the street, it is neither agreeable 
nor disagreeable as long practice has made me indifferent 
to it. 

When there is any doubt as to the terms being con- 
tradictory, the safest plan is to prefix "not" or "non" 
to the positive form. 

Terms which oppose each other but do not contradict 
are said to be opposite or contrary terms. The follow- 
ing list illustrate opposite terms : 

hot cold 

cool warm 

less greater 

wise foolish 

bitter sweet 

soft hard 

tall short 

agreeable disagreeable 

All these terms admit of a medium. In the case of hot 
or cold, for example, a substance need not necessarily 
be either. It may be warm or cool. 

Terms seem to be contradictory when it is a matter 
of quality, but opposite when it is a question of quantity 
or degree. 

11. PRIVATIVE AND NEGO-POSITIVE TERMS. 

A privative term is one which is positive in form but 
negative in meaning. Such words as blind, deaf, dumb, 



56 Logical Terms 

dead, maimed, orphaned, are privative terms, in that 
there is no negative prefix or suffix and yet they denote 
the absence of certain qualities. "Blind," for example, is 
positive in form, but denotes absence of sight. 

A nego-positive term is one which is negative in form 
but positive in meaning. Such terms as invaluable, un- 
loosed, immoral, indwell, are nego-positive because, 
though they have negative prefixes, yet they possess a 
certain positive meaning. "Invaluable," for instance, does 
not mean not-valuable, but very valuable. 

12. ABSOLUTE AND RELATIVE TERMS. 

An absolute term is one whose meaning becomes in- 
telligible without reference to other terms. Automobile, 
water, tree, house, book, are absolute terms. Any of 
them may be made clear to a child or a foreigner with- 
out special reference to other terms. For example, the 
child will recognize from certain common marks the 
automobile every time he sees it. The marks of tree, 
house, flower, are apparent to every one. 

A relative term is one which derives its meaning from 
its relation to some other term. Parent, teacher, shep- 
herd, monarch, eldest, cause, commander, are relative 
terms. For example, in explaining the meaning of 
"parent" to a foreigner, reference must be made to 
"child." The pairs of terms thus associated are spoken 
of as correlatives. Parent and child, teacher and pupil, 
shepherd and flock, monarch and subject, eldest and 
youngest, cause and effect, commander and army, are 
correlative terms. Either one of each pair is the corre- 



Absolute and Relative Terms 57 

late to the other, and every relative term needs its 
correlate to make its meaning clear. To say that a rela- 
tive term denotes an object which cannot be thought of 
without reference to some other object, is confusing, as 
it is quite impossible to think of any object without call- 
ing to mind some other object or notion. Fire calls to 
mind water; tree suggests shade, etc. 

13. OUTLINE. 

Logical Terms. 

(1) Meaning of term. 

(2) Categorematic and syncategorematic words. 

(3) Kinds of terms. 

Singular terms. 
General terms. 

(a) Collective terms. 

(b) Distributive terms. 
Concrete and abstract terms. 
Connotative and non-connotative terms. 
Positive and negative terms. 
Contradictory and opposite terms. 
Privative and nego-positive terms. 
Absolute and relative terms. 

14. SUMMARY. 

A logical term is a word or group of words denoting a definite 
notion. 

A singular term is a term which denotes one object or one 
attribute. 

A general term is a term which denotes an indefinite number 
of objects or attributes. 

General terms are collective or distributive. 

A collective term is a general term which indicates an indefi- 
nite number of objects considered as one whole. 

A distributive term is a general term which indicates an in- 



58 Logical Terms 

definite number of objects as a whole and also may be used to 
refer to each one of the group separately. 

A concrete term is a term, which denotes a thing. 

An abstract term is a term which denotes the attribute of a 
thing. 

A connotative term is one which denotes a subject and at the 
same time implies an attribute. 

A non-connotative term is one which denotes a subject only 
or implies an attribute only. 

A positive term is one which signifies the possession of certain 
attributes. 

A negative term is one which signifies the absence of certain 
attributes. 

In theory every positive term has its negative. As related 
to each other positive and negative terms are said to be con- 
tradictory. If one denotes a true notion then the other denotes 
a false notion. 

Some terms oppose each other but do not flatly contradict. 
As related to each other such terms are said to be opposite. 

A privative term is one which is positive in form but negative 
in meaning. 

A nego-positive term is one which is negative in form but 
positive in meaning. 

An absolute term is one whose meaning becomes intelligible 
without reference to other terms. 

A relative term is one which derives its meaning from its 
relation to some other term. 

15. ILLUSTRATIVE EXERCISES. 

(la) The words in italics are categoremaftic. 

(1) "Honesty is the best policy. 

(2) "A wise teacher never scolds." 

(3) "The woodcock has a long bill and eyes high up on 

the head." 
Note — If there is any doubt as to such words as never, on, 
etc., being syncategorematic, attempt to use them as subject or 
predicate of a proposition; e. g., John is never. 



Illustrative Exercises 59 

(lb) Underscore the categorematic words in the following: 

(1) "Socrates was the greatest teacher of pagan times." 

(2) "Play is nature's way of teaching a child how to 

work." 

(3) "A man may be what he chooses if he is willing to 

pay the price." 
(2a) In the following, words enclosed in parentheses are 
logical terms : 

(1) ("All men) are (mortal.") 

(2) ("The law of identity) is (one of the primary laws 

of thought.") 

(3) ("Judging) is (the process of conjoining and dis- 

joining notions.") 

(2b) Indicate the logical terms in the sentences under lb. 

(3a) The logical characteristics of the term teacher are 
(1) general term, (2) distributive term, (3) concrete term, (4) 
connotative term, (5) positive term, (6) relative term. 

(3b) The logical characteristics of other terms are as 
follows : 

(1) Goodness — general, abstract, non-connotative, posi- 

tive, abstract. 

(2) Soft — general, concrete, non-connotative, positive, 

"hard" is its opposite, "not-soft" is its contradictory, 
absolute. 

(3) Disagreeable — general, concrete, non-connotative, 

"agreeable" is its opposite, "not-disagreeable" is its 
contradictory, nego-positive, absolute. 

(4) Aristotle — singular, concrete, non-connotative, positive, 

absolute. 

(5) Class — general, collective, concrete, connotative, posi- 

tive, relative. 
(3c) Give the logical characteristics of the following terms: 
justice, Abraham Lincoln, tree, library, America, president, prin- 
ciple, sympathy, dumb, nation. 

16. REVIEW QUESTIONS. 

(1) What is the connection between logical thinking and 
language ? 



60 Logical Terms 

(2) Why is man a categorematic word? 

(3) Why is beautifully syncategorematic? 

(4) Distinguish between singular and general terms. 

(5) Show how a collective term may be used in a distributive 
sense. 

(6) Why are the words tree and book distributive? 

(7) Distinguish between concrete and abstract terms. 

(8) Define and illustrate a non-connotative term. 

(9) Why are concrete general terms connotative? 

(10) Distinguish between positive and privative terms. 

(11) Why is not the word immoral negative? 

(12) Give the opposite of "hot." What is the contradictory 
of "hot"? 

(13) Distinguish by definition and illustration between rela- 
tive and absolute terms. 

(14) What is the correlate of the word effect? 

17. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Is it possible to think independent of language? 

(2) May words be spoken or written without thought? Il- 
lustrate. 

(3) Are categorematic words always logical terms? 

(4) Must all the words of a logical term be categorematic? 

(5) Are pronouns and auxiliary verbs categorematic? 

(6) Indicate the logical connection between the terms of a 
proposition and the termini of a railroad. 

(7) Show that attribute is a broader term than quality. 

(8) Is the word Washington general or singular? Give 
reasons. 

(9) Make the word dog a singular term. 

(10) Give an illustration where the word class would not be 
collective. 

(11) "All the members of the baseball team are star players." 
How has the term star players been used, collectively or dis- 
tributive^ ? 

(12) Why may the term New York City be connotative to a 
New Yorker and non-connotative to a Patagonian? 



Questions for Original Thought 61 

(13) So far as your present knowledge of the martyred 
president Abraham Lincoln is concerned, is the term, Abraham 
Lincoln connotative or non-connotative ? 

(14) Are non-connotative terms always singular? Illustrate. 

(15) Are singular terms always non-connotative? 

(16) What is the differenece in meaning between immoral 
and unmoral, disagreeable and not-agreeable? 

(17) Why is immoral a nego-positive term while unmoral 
is negative? 

(18) What is the contradictory of the opposite of wise? 

(19) Show that there is some ground for believing all terms 
to be relative. 

(20) Is army a relative term? If "army" were used so as to 
be distributive in nature would it then be general or collective? 

(21) Why should the pronoun be ignored by the logician? 

(22) Show the difference between thing and subject. 

(23) Argue to the effect that no term can be non-contotative. 



CHAPTER 5. 

THE EXTENSION AND INTENSION OF TERMS. 

1. TWO-FOLD FUNCTION OF CONNOTATIVE TERMS. 
(See page 52). 

It has been indicated that a connotative term is one 
which possesses the double function of signifying a 
subject as well as an attribute. It may be observed here 
that an attribute of a notion is any mark, property or 
characteristic of that notion. Attribute, then, repre- 
sents quality, relation or quantity. By a subject is 
meant anything which possesses attributes. Most sub- 
jects stand for objects and most attributes are qualities; 
consequently, for the sake of simplicity, we may use 
subject and object interchangeably; likewise, attribute 
and quality. 

A connotative term, therefore, denotes an object at 
the same time it implies a quality. To illustrate: The 
symbol man stands for the various individual men of 
the world, such as Lincoln, Washington, Alfred the 
Great, etc., or for certain qualities like rationality, power 
of speech and power of locomotion. The connotative 
term teacher may be used to denote Socrates, Pestalozzi, 
Thomas Arnold, or connote such qualities as ability to 
instruct, sympathy, and scholarship. The term planet 
stands for such objects as Venus, Earth, and Mars, and 
for such qualities as rotation upon axis, revolution about 
sun, and opaque or semi-opaque bodies. In each of the 

62 



Two-fold Function of Connotative Terms 63 

three illustrations the term is employed in the two- fold 
sense of denoting objects and of implying qualities. 

2. EXTENSION AND INTENSION DEFINED. 

This double function of connotative terms furnishes 
an important topic for the student of logic — the Exten- 
sion and Intension of Terms. In short, some authorities 
claim that to master the extension and intension of terms 
is virtually to master the entire subject of logic. Though 
this position may be an exaggerated one, yet it tends to 
emphasize the importance of the topic. 

A term is used in extension when it is employed with 
reference to the objects for which the term stands. 

When the term triangle is used to refer to the objects 
isosceles triangle, scalene triangle, right triangle, it is 
employed in extension. 

A term is used in intension when it is employed with 
reference to the attributes for which the term stands. 

The term triangle is employed in intension when we use 
it to refer to the qualities, three sided and three angled. 

3. EXTENDED COMPARISON OF EXTENSION AND IN- 

TENSION. 

A connotative term seems to be two dimensional — 
it has extent or length and intent or depth. 

"Extension consists of the things to which the term 
applies," while "intension consists of the properties 
which the term implies." 

Extension is quantitative, while intension is qualita- 
tive. An extensional use means to point out or num- 



64 The Extension and Intension of Terms 

ber objects, while an intensional use means to describe 
by naming qualities. To name is to use a term in ex- 
tension — to describe is to use a term in intension. 

To divide a term into its kinds we must regard it in an 
extensional sense ; e. g., the term man may be divided into 
Caucasian, Mongolian, Malay, Ethiopian, American Indian. 

To define a term we must regard it in an intensional 
sense; e. g., man is a rational animal. 

Etymologically considered extension means to stretch 
out, intension, to stretch within. To use a term exten- 
sionally one must look out. To use a term intensionally 
one must look in. 

In attempting to use a term in extension we may ask 
ourselves the question, "What are the kinds?" or "To 
what objects may the term be applied?" While if we 
would use a term in intension the question should be, 
"What does it mean?" or "What are the qualities?" 
Let us, for example, use the term metal in the two 
senses, first in extension, second in intension. Question: 
To what objects may the term metal be applied? An- 
swer: Metal may be applied to the objects silver, gold 
and iron. Thus has metal been employed in extension. 

Question: What are the qualities of metal ? Answer: 
The qualities are element, metallic lustre, good conductor 
of heat and electricity. Thus has metal been used in 
intension. 

Note. Since an attribute is anything which belongs 
to a subject, then the parts of a subject must be classed 
as attributes. Hence, a term is used intensionally when 
reference is made to its parts. 



List of Connotative Terms 65 

4. A LIST OF CONNOTATIVE TERMS USED IN EXTEN- 
SION AND INTENSION. 

The Term. Extensional Use. Intensional Use. 

[roots, branches, trunk, 
tree. maple, oak, beech. «j or 

(woody-fiber, sap, bark. 

house. stone, brick, cement, foundation, frame-work, 

roof. 

dog. shepherd, fox terrier, carnivorous, quadruped, 

bull. propensity to bark. 

book. textbook, dictionary, cover, leaves, binding, 

encyclopaedia. 

quadrilateral, trapezium, trapezoid, four sides, four angles, 
parallelogram. limited plane. 

logic. theoretical logic, ap- science of thinking, art of 

plied logic, educa- right thinking, treats of 
tional logic. laws of thought. 

star. Sirius, Arcturus, heavenly body, gives light 

Vega. and heat, twinkles. 

force. gravitation, molecular, [produces motion 

atomic. -{changes motion 

(^destroys motion. 

term. general, singular, word or group of words, 

non-connotative. definite idea. 

government. monarchy, aristocracy, body of people, estab- 
democracy. lished form of law, 

banded together for mu- 
tual protection. 

bird. crow, robin, pigeon, biped, feathered, winged. 



66 The Extension and Intension of Terms 

5 OTHER FORMS OF EXPRESSION FOR EXTENSION 
AND INTENSION. 



Extension. 


Intension. 


comprehension 


content 


extent 


intent 


breadth 


depth 


denotation 


connotation 


application 


implication 



Formerly the words extension and intension were ap- 
plied to concepts while denotation and connotation were 
applied to terms representing the concepts, but now the 
words are interchangeable. Denotation, the noun, and 
denote, the verb, signify, etymologically, a marking off. 
To denote is to mark off or indicate the objects or classes of 
objects for which the term stands. Connotation, the noun, 
and connote, the verb, signify to mark along with. To 
connote is to mark along with the object, its attributes. 
The terms which should be remembered are 

extension f intension 

or [» and *J or 

denotation J I connotation 

6. LAW OF VARIATION IN EXTENSION AND INTEN- 
SION. 

It has been noted that the intension of a term has 
reference to its qualities while extension considers its 
application to various objects. It may be wise to ex- 
periment with the extension and the intension of certain 
terms as types with a view of ascertaining how the two 
ideas are related to each other. For the sake of defi- 
niteness let us make use of the following scheme : 



The Law of Variation in Extension and Intension 67 



Intensional 

(1) four sides 

(2) parallel sides 

(3) equal sides 

(4) right angles 

(1) four sides 

(2) parallel sides L 

(3) equal sides 



I. 



common 
qualities of 



common 
qualities of 



(1) four sides 1 common 

(2) parallel sides \ qualities of 



(1) four sides 



( 1 ) heavenly body 



common 
quality of 



II. 



) common 
j quality of 



(1) heavenly body ) common 

(2) self-luminous ( qualities of 



Extensional 
} (1) squares 



(1) squares 

(2) rhombs 

(1) squares 

(2) rhombs 

(3) rectangles 

(4) rhomboids 

(1) squares 

(2) rhombs 

(3) rectangles 

(4) rhomboids 

(5) trapezoids 

(6) trapeziums 



(1) nebulae 

(2) fixed stars 

(3) sun 

(4) comets 

(5) meteors 

(6) moon 

(1) nebulae 

(2) fixed stars 

(3) sun 

(4) comets 



68 



The Extension and Intension of Terms 



common 
qualities 



J 



(i) 

(2) 

(3) 



nebulae 
fixed stars 
sun 



common 
*" qualities of 



common 



qualities of | 



(i) 

(2) 



nebulae 
fixed stars 



(i) nebulae 



(i) heavenly body 

(2) self-luminous 

(3) fixed 

(1) heavenly body 

(2) self-luminous 

(3) fixed 

(4) twinkle 

(1) heavenly body 

(2) self-luminous 

(3) fixed 

(4) twinkle 

(5) foggy 

In considering the first illustration we observe that as 
the number of qualities is decreased, the number of ob- 
jects increases. While in the second example as the 
qualities are increased, the number of objects decreases. 
It would appear from this that the intension and exten- 
sion of a term are inversely related to each other. As 
the one increases the other decreases and vice versa. 
It is customary to state this relation in the form of a 
law known as the law of variation. "As the intension 
of a term is increased its extension is decreased and vice 
versa/' or the extension and intension of a term vary in 
an inverse ratio to each other. To further illustrate: 
this book refers to a large number of objects; add to the 
qualities of book those of text book and the application is 
much reduced. In other words as we increase the intension, 
the extension is diminished. Increase the intension 
further by adding the quality English text book and the 
extension becomes still less. 



Two Important Facts in the Law of Variation 6g 

6a. TWO IMPORTANT FACTS IN THE LAW OF VARIA- 
TION. 

In studying the law of variation two facts are espe- 
cially evident, (i) The law applies only to a series of 
terms representing notions of the same family. The ex- 
tension and intension of "text book," for example, could 
not be compared with the extension and intension of 
"house" as they belong to a different class of words, the 
genus of text book being book, while the genus of house 
is building. 

To illustrate the law of variation, determine upon any 
class name, then think of its proximate genus (the next 
higher-up class to which it belongs). Continue this till 
the series is sufficiently complete to illustrate the law. 
Or proceed in the opposite direction. That is, after se- 
lecting the class name think of the next lower term in 
the class and thus continue till series is complete. Il- 
lustration: The class name man is determined upon; the 
proximate genus of man is biped, the proximate genus 
of biped is animal, and so on. Or thinking downward: 
a proximate species of man is white man, of white man, 
European, etc. 

Thus the series: 

animal 

biped 

man 

white man 

European 

(2) As a second fact: the increase and decrease is 
not a mathematical one. That is, by doubling the ex- 



yo The Extension and Intension of Terms 

tension the intension is not halved. Or if the intension 
is decreased by one quality the extension is not neces- 
sarily increased by one object. Thus "man" stands for one 
billion seven hundred million beings or objects. De- 
crease the intension of "man" by the one quality of ra- 
tionality and the extension would include all bipeds — 
many billion objects. 

6b. THE LAW OF VARIATION DIAGRAM MATICALLY 
ILLUSTRATED. 

In a general way lines may be used to represent the 
variation in extension and intension. For example: we 
may let a line an inch long represent the extension of 
man, one two inches long represent the extension of 
biped, three inches long represent the extension of 
animal, etc. While on the other hand, if a line an inch 
long represents the intension of man, a line one-half inch 
long may be used to represent the intension of biped, one 
a quarter of an inch long to represent the intension 
of animal, etc. The following illustrates this scheme in 
connection with another series of words: 

Extension Intension 

barn 

building 

structure 

object ' 

In the foregoing scheme building refers to a greater 
number of objects than bam, hence the line under exten- 
sion representing building should be longer than the line 
for barn. Likewise structure, referring to a greater num- 
ber of objects than building, is represented by a longer 



Law of Variation Diagrammatic ally Illustrated Ji 

line. Thus when the series is viewed from top to bottom 
a gradual increase in extension is noted. Giving atten- 
tion to the intensional use of the series we note that 
building has fewer qualities than barn, structure fewer 
than building and object fewer than structure. There- 
fore, from top to bottom, the intension of the terms 
gradually decreases. 

The variation may be made still more apparent if 
triangles are used, one triangle being placed upon the 
other, vertex to base, like the following: 




EyzleriiSi 



"Biped" is written near the base or in the broadest part 
of the extension triangle because it denotes the greatest 
number of objects, and is, therefore, broadest in exten- 
sion. "Man" occupies a narrower part of the extension 
triangle because it refers to fewer objects or is narrower 
in extension than "biped." "Arnold" occupies the nar- 
rowest part of the extension triangle because it is the nar- 
rowest in extension. On the other hand "Arnold" occu- 
pies the broadest part of the intension triangle because in- 
tensionally it possesses more qualities than the others, 



*]2 The Extension and Intension of Terms 

while "biped," having the least depth in intension or pos- 
sessing the fewest qualities, occupies the narrowest por- 
tion of the intension triangle. 

7. OUTLINE. 

The Extension and Intension of Terms. 

1. Two-fold Function of Connotative Terms. 

2. Extension and Intension Defined. 

3. Extended Comparison of Extension and Intension. 

4. A List of Connotative Terms used in Extension and 
Intension. 

5. Other Forms of Expression for Extension and Intension. 

6. Law of Variation in Extension and Intension. 
6a. Two Important Facts in the Law of Variation. 

6b. The Law of Variation Diagrammatically Illustrated. 

8. SUMMARY. 

1. Connotative terms are used in a two-fold sense : first, to 
denote objects;, second, to imply qualities. 

2. A term is used in extension when it is employed with 
reference to the objects for which the term stands. A term is 
used in intension when . it is employed with reference to the 
qualities for which the term stands. 

3. The answer to either of the following questions will lead 
one to use any term in extension: First, what are the kinds? 
or second, to what objects may the term be applied? 

The answer to either of the following questions will lead to 
the use of any term in intension : First, what does it mean ? 
or second, what are the qualities? 

4. To illustrate extension and intension it is best to use the 
class-names in every day speech. 

5. The word denotation is commonly used for extension and 
connotation for intension. 

6. "As the intension of a term is increased its extension is 
decreased and vice versa," is a statement of the Law of Vari- 
ation in the extension and intension of terms. 

6a. The law of variation applies only to a series of terms 
representing notions of the same class or family, the words 



Summary 73 

being arranged in a species-genus order. The increase and de- 
crease of the extension and intension of a series is not propor- 
tional. 

6b. The law of variation is best explained by using two 
triangles, one super-imposed upon the other vertex to base and 
base to vertex. 

9. ILLUSTRATIVE EXERCISES. 

la. Employ the following terms in extension — European, 
flower, term, truth. 

("Russian [lily 

European-] Englishman nower-j rose 

[Scotchman (pansy 

[singular Truth has no extension. Since 

term-J distributive it refers to a quality only, it 

[collective is non-connotative. 

lb. Employ the following in extension — grain, rock, soil, 
precious stone. 
2a. Use intensionally bird, quadruped, letter, John. 

[two feet ("four feet 

bird-! ability to fly quadruped-/ back bone 

[^feathers . I hairy covering 

("heading John has no intension. Since 

letter-jbody it refers to an object only, it 

[complimentary close is non-connotative. 

2b. Use the following in intension — word, table, purity, gov- 
ernment. 

3a. The use of a term in extension follows when attempting 
to answer two questions: First, what are the kinds? Second, 
to what objects may the term be applied? Make application of 
this with reference to the term man. 

1. What are the kinds of men? Caucasian, Malay, Mongo- 
lian, Ethiopian, Redman. 

2. To what objects does the term man refer? George Wash- 
ington, Chas. Hughes, John Smith. 



74 



The Extension and Intension of Terms 



In both 1 and 2 the word man is used to denote objects, hence 
it is employed in extension. 

3b. Use the term vegetable in extension by answering the two 
questions in 3a. 

4a. Decrease one by one the qualities of some common object 
with a view of noting how when the intension is decreased the 
extension is increased. 



Intension 
binding 
leaves 
cover 

printed matter 
designed for instruction 
instruction in arithmetic 

binding 

leaves 

cover 

printed matter 

designed for instruction 

binding 

leaves 

cover 

printed matter 



binding 
leaves 



Extension 



school arithmetic 



school arithmetic 
school grammar 
school speller, etc. 

"school arithmetic 
school grammar 
school speller, etc. 
encyclopaedia 
novel 

'school arithmetic 
school grammar 
school speller, etc. 
encyclopaedia 
novel 
note book 



4b. With a view of noting how when the intension is de- 
creased the extension is increased, decrease one by one the 
common qualities of peach tree. 

5a. In the following series what word could be substituted for 
"mammal" and why? Being, organized being, animal, vertebrate, 
mammal. Answer: Fish, reptile, or bird; because there are at 



Illustrative Exercises 75 

least seven classes of animals which belong to the vertebrate fam- 
ily, any one of which could be used to complete the series. 

5b. Form a series of which "Baldwin apple" has the narrow- 
est extension. What terms may be substituted for "Baldwin 
apple ?" 

6a. In a series of which "pupil" is a member show that the 
increase and decrease is not proportional. The series: logic 
pupil, pupil, youth, human being, being. In decreasing the inten- 
sion of "logic pupil"- by dropping the one quality, logic, the ex- 
tension is made larger by many more than one, as "pupil" repre- 
sents many more objects than "logic pupil." Therefore, the in- 
crease is not in proportion to the decrease. 

6b. In a series in which "ruler" appears, show that the in- 
crease and decrease is not proportional. 

7. From the following list select the proper words of the 
series; arrange them; draw and name the triangles: 

Caesar, brute, man, Roman, American, biped, sensuous being, 
animal, individual. 

10. REVIEW QUESTIONS. 

1. What is a connotative term? Illustrate. 

2. Which is the broader term, quality or attribute? Why? 

3. When is a term used in extension? 

4. Use the term triangle in intension. 

5. As an aid to using a term in extension or intension what 
questions may one ask himself? 

6. By asking these questions use the term clock in both ex- 
tension and intension. 

7. By experimenting with the qualities of a rectangle show 
that as the intension is decreased the extension is increased. 

8. Write a list of five connotative terms. Prove that they 
are connotative by illustrating their extension and intension. 

9. The term metal < connotes ( su ch qualities as element, metal- 
lic lustre, conductor of heat and electricity. In the foregoing 
which of the two words following the brace should be used? 
Give reasons. 

10. State the law of variation in two ways. 



y6 The Extension and Intension of Terms 

11. As one studies the law of variation what two facts are 
especially evident? Explain fully. 

12. For the purpose of illustrating the law of variation form a 
series of which desk is a member. Draw and name the tri- 
angles. 

11. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

1. Which is the broader term, subject or object? Prove it. 

2. If a term like Caesar is given extension does it become a 
general term? Why? 

3. Using "man" as a member of each, arrange at least three 
different series. 

4. Why may it be said that a connotative term is two dimen- 
sional ? 

5. Is there a word which has a broader extension than 
"being"? Why? 

6. Prove that youth has less intension than human being. 

7. Devise a series of words in which the variation is propor- 
tional. 

8. Advance arguments supporting the hypothesis that the term 
John has neither extension nor intension. 

9. Suggest arguments to prove that "George Washington" has 
both extension and intension. 



CHAPTER 6. 

DEFINITION 

1. IMPORTANCE. 

To be clear, cogent,' concise and consistent is to be 
logical. Reference has been made to a striking tendency 
on the part of writers and speakers to use words loosely. 
It is a noticeable fact that scholars generally aim to be 
profound rather than clear, philosophical rather than' 
pointed. 

In the use of text books more or less pedagogical 
these are the common complaints : "I don't understand 
what he means" or "You have to read so much to get 
so little." This condition gives to the topic of definition 
a prominence which cannot be overlooked by those who 
are seeking the truth; because the definition is the clear- 
est, briefest and altogether the most satisfactory way of 
describing an idea. Likewise the habit of defining any 
doubtful term reduces to a minimum the possibility of 
misunderstanding. 

The subject must appeal strongly to the instructor, as 
he, above all others, should make his work stand for 
clearness, pointedness and continuity. 

2. THE PREDICABLE8. 

A predicable is a term which can be affirmed or predi- 
cated of any subject. In the proposition, "A man is a 
rational animal," the term "rational animal" is a pred- 

77 



yS Definition 

icable, because it can be affirmed of the subject man. 
To gain a clear knowledge of the definition it is quite 
necessary to understand the five predicables which we 
shall consider in the following order : 

1. Genus. 

2. Species. 

3. Differentia (difference). 

4. Property. 

5. Accident. 

(1) Genus and (2) Species. 

Genus and species are relative terms and can best be 
denned together. 

A genus is a term which stands for two or more sub- 
ordinate classes. 

A species is a term which represents one of the sub- 
ordinate classes. 

The genus may be subdivided into species ; the species 
together form the genus. . 

To illustrate: The term man stands for five sub- 
ordinate classes or species, as white, black, brown, yellow 
and red. "Man" is, therefore, a genus, while "white man" 
and "black man," etc., are species. The term "polygon" is 
a genus with reference to "trigon," "tetragon," "penta- 
gon," etc., while "trigon" is a species of "polygon." 

Any given genus may be a species of some higher 
class. That is, "man," which is a genus with reference 
to the kinds of men, is a species of the higher class 
"biped," while "biped" is a species of "animal," "animal" 
a species of "organized being," "organized being" of 
"material being," "material being" of "being." But here 



The Predicables 79 

we stop, as there is no higher grade to which "being" 
can be referred. This highest genus takes the name of 
summum genus. 

Similarly any given species may be a genus of some 
lower class. "White man," for example, which is a spe- 
cies of "man," is a genus of "American," Englishman," 
"German," Frenchman," etc. "American" is a genus of 
"New Yorker," "Californian," etc., while "New Yorker" 
is s a genus of "Smith of Jamaica." This last term is an in- 
dividual and cannot be subdivided. It represents the lowest 
possible species and is referred to in logic as infima species. 

It is obvious that the highest genus cannot become a 
species, neither can the lowest species become a genus. 

Proximate Genus. 

The proximate genus is the next class above. To illus- 
trate: "Animal" is a genus of "man," but "biped" is the 
proximate genus of "man." "Quadrilateral" is the genus 
of "square," but "rectangle" is the proximate genus. The 
next class above "trigon" is polygon not figure. Hence 
"polygon" is the proximate genus of "trigon." 

Genus and Species of Natural History. 

In natural history the following terms are used to de- 
note the various grades of kinship in any scheme of 
classification: (1) kingdom, (2) class, (3) order, (4) 
family, (5) genus, (6) species, (7) variety, (8) the in- 
dividual thing. Here "genus" and "species" are absolute 
not relative and occupy a fixed place in the scheme, 
while from a logical viewpoint any of the grades indi- 
cated between the lowest and highest would be the species 



80 Definition 

of the next higher grade or a genus of the next lower; 
e. g., order is a species of "class," while it is the genus of 
"family." 

Genus, a Double Meaning. 

We recall that any class name or genus has a double 
use, extensional and intensional. When considered from 
the standpoint of its extension, a genus represents a group 
of objects or is mathematical in its application, but when 
used in an intensional sense it represents a group of 
qualities or is logical in its application. 

Considered extensionally the genus refers to a larger 
number of objects than the species. But when viewed 
intensionally the species refers to more qualities than 
the genus. This was made clear when discussing the 
law of variation in the extension and intension of terms. 

(3) Differentia. 

The differentia of a term is that attribute which dis- 
tinguishes a given species from all the other species of 
the genus. 

It has been observed that the species refers to more 
qualities than the genus. In fact, it represents all the 
attributes of the genus plus those which distinguish the 
particular species from the other species of the genus. 
These additional qualities are the differentiae of the 
particular species. 

To Illustrate: 

The attribute which distinguishes man from the other 
bipeds of the world is his rationality. That which dis- 
tinguishes the rectangle from the other parallelograms 



The Predicables 81 

is its four right angles. The attributes rationality and 
right angles are differentiae. 

(4) Property. 

A property of a term is any attribute which helps to 
make the term what it is. Thus "consciousness" is a 
property of man, "binding" a property of book, "angles" a 
property of triangle. Deprive the terms of these attri- 
butes and their true nature is altered. 

A differentia is a property according to the foregoing 
definition. However, Jevons defines "property" as "Any 
quality which is common to the whole of a class, but is not 
necessary to mark out the class from other classes." This 
viewpoint excludes "differentia" from the notion of prop- 
erty. The difference in opinion is of slight importance. 

(5) Accident. 

An accident of a term is any attribute zvhich does' 
not help to make the term what it is. It may indif- 
ferently belong or not belong to the term. Deprive a 
term of an accident and the nature of the term remains 
unchanged. Thus, a teacher's position, a man's watch, 
the fact that the angle is one of 80 ° are all accidents. 

It is obvious that a property is a constant attribute 
while an accident is variable. This gives to the former a 
universal validity while the latter is more or less shifting 
and uncertain. All triangles must have three angles 
(property) while the value of each angle in degrees 
(accident) admits of unlimited variation. 

Some logicians divide accidents into separable and 
inseparable. A man's hat would be a separable accident 
while his birthplace would be an inseparable accident. 



82 Definition 

Five Predicables Illustrated. 

In the following brief descriptions the five predicables 
are designated: 

(species) (genus) (differentia) 



(1) This rectangle is a parallelogram with four right angles 
(accident) 



its longer sides being ten inches. 

(species) (differentia) (prox. genus) 



(2) This man is a rational biped with the 

(property) (accident) 



power of locomotion and a ruddy complexion. 

(species) (genus) (differentia) (property) 



(3) A trigon is a polygon of three sides and three angles, 
(accident) 

the sum of the angles being equal to two right angles. 



3. THE NATURE OF A DEFINITION. 

It will be remembered that an individual notion is a 
notion of a single thing or attribute, while a general 
notion is a notion of a class of things or a group of at- 
tributes. A term which represents an individual notion 
is known as a singular term, while a term which stands 
for a general notion is referred to as a general term. 

One may explain the meaning of a singular term which 
stands for one thing by enumerating its various attri-, 
butes. For example, such attributes as a piercing bark, 
a yellow color, intelligent, companionable, a strong liking 
for sweetmeats, explain the meaning of the singular term 
"Fido." Likewise we may explain the meaning of a gen- 
eral term by enumerating its attributes. To illustrate: 



The Nature of a Definition 83 

power of speech, rationality, ability to laugh, etc., explain 
the meaning of the general term man. The explanation of 
the singular term fits only Fido. There is probably no 
other dog in the world just like Fido. But the explana- 
tion of the general term man may be applied to all men. 
A brief enumeration of attributes which may be ap- 
plied to a class of things often takes the form of a defi- 
nition. The word definition comes from the word 
definire, meaning to limit or fix the bounds of. 

A definition, then, consists of the enumeration of -such 
attributes as distinguish a term from all other terms. In 
this sense it would seem that the singular term Fido, as 
well as the general term man, admits of definition, but 
it is usual for logicians to confine definition to the general 
term. Singular terms may be described; general terms, 
defined. 

A Definition of> Definition. 

A definition of a term is a statement of its meaning by 
enumerating its characteristic attributes. 

That the enumeration must be in terms of its dis- 
tinguishing or characteristic attributes is implied in the 
derivation of the term definition. The attributes must 
establish limits or bounds, just as a line fence limits a 
land owner's possessions. To indicate that man is a crea- 
ture possessing the power of locomotion, sense of sight 
and ability to eat, is surely not a definition, as the marks 
are not characteristic of men only. These attributes set 
no boundary between man and horse, consequently the 
statement is a faulty description of man, not a definition. 



84 Definition 

But when the enumeration includes such attributes as 
power of speech, rationality and ability to laugh, then does 
the description become a definition. To put it differently : 
A definition is a description of a term by means of its dis- 
tinguishing attributes. This statement may be considered 
a definition of man, though somewhat faulty : "A man is 
a creature who is rational and who possesses the power 
of speech and ability to laugh." 

4. DEFINITION AND DIVISION COMPARED. 

We have learned that general terms when connotative 
may be used extensionally or intensionally. 

A definition indicates the intensional nature of a term, 
while a statement which points out the extensional na- 
ture of a term is known as logical division. More briefly : 
A definition is an intensional statement of the nature of 
the term, while logical division is an extensional state- 
ment of the nature of the term. 

To illustrate: The following statements are defini- 
tions : 

(i) A dog is a domesticated quadruped of the genus 
canis and given to barking. 

(2) A quadrilateral is a rectilinear figure of four 

sides. 

(3) Soil is a substance composed of pulverized rock 

and decayed vegetable matter in which plants 
will grow. 
The following represent Logical Division : 

(1) Dogs are divided into hounds, terriers, bull, etc. 



Definition and Division Compared 85 

(2) The kinds of quadrilaterals are trapeziums, 

trapezoids and parallelograms. 

(3) The various soils are loam, sand, clay, muck, etc. 

5. THE KINDS OF DEFINITIONS. 

Generally speaking there are three kinds of definitions, 
namely, (1) Etymological, (2) Descriptive, (3) Logical. 1 

(1) An etymological definition is one based upon the 
derivation of the term. 

This kind of a definition, which gives merely the mean- 
ing of the symbol, is sometimes called a nominal or verbal 
definition; while a real definition is regarded as one 
which gives the meaning of the notion for which the sym- 
bol stands. The modern logician is inclined to ignore this 
classification on the argument that to make a distinction 
between a symbol and the notion it symbolizes is simply 
to misunderstand the relation which exists between them. 
If the definition does not agree with the thing then it 
cannot correctly explain the term which represents the 
thing. Define correctly the term and one has defined 
correctly the notion signified by the term. 

The attributes of a term may be separated into three 
classes: differentia, property and accident. It would ap- 
pear possible, therefore, to define a term by enumerating 
the accidents only or by enumerating the properties, or, 
finally, by stating the differentiae. But if the enumera- 
tion is confined to accidents the chances are that the state- 
ment will be a description, not a definition, as accidents 
are seldom sufficiently characteristic to determine the 



* Hyslop's Elements of Logic (1901), page 100. 



86 Definition 

boundaries of a term. This leaves open two distinct ways 
of defining a term: First, by naming the properties or 
properties and accidents only; second, by stating the dif- 
ferentiae only. The former kind is the so-called descrip- 
tive definition, while the latter is the logical. 

(2) A descriptive definition of a term is a description 
of its nature by means of its properties and accidents. 

(3) A logical definition of a term is a description of 
its nature by means of its digerentice. 

The Three Kinds of Definitions Illustrated and 
Compared. 
Etymological Definition of Trigon. 

A trigon is a figure of three corners. 
Descriptive : 

A trigon is a figure which has three sides and three 
angles, the sum of the latter being equal to two 
right angles. 
Logical : 

A trigon is a polygon of three angles. 
It is seen that an etymological definition is simply a 
root-word analysis. In' the case of trigon, the prefix 
comes from the Greek, meaning three, while the root-word 
comes from the Greek meaning corner. 

The descriptive definition of trigon names the proper- 
ties, "three sides and three angles" (differentiae) and the 
accident, "the sum of the angles of which equals two right 
angles." 

The logical definition of trigon simply states the proxi- 
mate genus, "polygon," and the differentia, "three angles." 



When Definitions Are Serviceable 87 

6. WHEN THE THREE KINDS OF DEFINITIONS ARE 
SERVICEABLE. 

The etymological definition is helpful in furnishing a 
cue for remembering the descriptive and logical defini- 
tions. It also leads to precision of expression — the right 
word in the right place. Here is where the knowledge of 
a foreign language, particularly Latin, is helpful. 

The descriptive definition is best adapted to the child- 
mind. Children think in the large ; are not given to hair- 
splitting discriminations, and, therefore, many character- 
istic marks must be mentioned in order to insure a 
mastery of the content. With children the logical defini- 
tion is often too brief to be clear. For example, it is easy 
to see which of the following definitions would be better 
adapted to the child-mind. Logical: A square is an 
equilateral rectangle. Descriptive: A square is a figure 
of four equal sides and four right angles. 

The logical definition may be introduced to the student 
of the secondary school. 

Few exercises are better adapted to the development of 
powers of discrimination and precision than practice in 
defining logically the common terms of every-day life. 
For example: "A book is a pack of paper-sheets bound 
together." "A chair is a piece of furniture with back and 
seat, designed for the seating of one person." "A lead 
pencil is a cylindrical writing implement with lead through 
the center." "A door is an obstacle designed to swing in 
and out to open and close an entrance." "An eraser is 
an implement made to rub out written or printed char- 
acters." 



88 Definition 

These definitions, coming from training school stu- 
dents, are not above criticism, yet they illustrate the point 
in hand. 

7. THE RULES OF LOGICAL DEFINITION. 

Five rules summarize the requirements to which a 
logical definition must conform. 

First Rule. 

A logical definition should state the essential attributes 
of the species defined. 

This means that a logical definition should contain the 
species, the proximate genus and the differentia. As 
the terms species, genus and differentia have been 
explained, it will be sufficient to briefly illustrate this 
rule. 

Logical According to the First Rule. 
species genus differentia 



(1) A bird is a biped with feathers. 

species genus differentia 



(2) A mascot is a person supposed to bring good luck, 
species genus differentia 



(3) Religion is a system of faith and worship, 
species genus differentia 



(4) A moonbeam is a ray of light from the moon. 
Illogical According to the First Rule. 
(i) A man is a rational animal. 

("Biped" is the proximate genus, not "animal.") 



The Rules of Logical Definition 89 

(2) A connotative term always denotes both an ob- 
ject and an attribute. 

(No genus.) 

(3) A trigon is a polygon. 
(No differentia.) 

(4) It is a term which denotes an indefinite number 
of objects or attributes. 

(No species.) 
The Foregoing Illogical Definitions Made Logical. 

(1) A man is a rational biped. 

(2) A connotative term is a term which denotes both 
an object and an attribute. 

(3) A trigon is a polygon of three angles. 

(4) A general term is a term which denotes an indefi- 
nite number of objects or attributes. 

Second Rule. 

A logical definition should be exactly equivalent to the 
species defined. 

This means that the species must equal the genus plus the 
differentia or the subject and predicate of the definition 
must be co-extensive — of the same bigness. The subject 
must refer to the same number of objects as the predicate. 

A man upon the witness stand makes the declaration 
that he will testify to the truth, the whole truth and 
nothing but the truth. A logical definition must contain 
the species, the whole species and nothing but the species. 
If the definition does not include all the species, it is too 
narrow; while on the other hand, if it includes other 
species of the genus it is too broad. 



go Definition 

An excellent test of this second requirement is to inter- 
change subject and predicate. If the interchanged prop- 
osition means the same as the original then the conditions 
have been met. To illustrate: Original — A trigon is a 
polygon of three angles. Interchanged — A polygon of 
three angles is a trigon. 

The very best way of making the definition conform to 
this rule is to put to oneself these three questions: i. 
Does it include all of the species? 2. Does it exclude all 
other species of the genus? 3. Has it any unnecessary 
marks ? 

To exemplify: Let us ask the three questions rela- 
tive to the following logical definitions : 

(1) A parallelogram is a quadrilateral whose oppo- 
site sides are parallel. 

(2) A bird is a biped with feathers. 
Questions: 

( 1 ) Does the definition include all the parallelograms ? 
Yes. Does it exclude all other quadrilaterals? Yes. 
Are there any unnecessary marks ? No. 

(2) Does it include all birds? Yes. Does it exclude 
all other bipeds ? Yes. Any unnecessary marks? No. 

Illogical According to the Second Rule. 

(1) A man is a vertebrate animal. 

(Too broad. Does not exclude other species of the 
genus, such as horses, dogs, etc.) 

(2) A barn is a building where horses are kept. 
(Too narrow. Does not include all of the species, such 

as cow barn.) 



The Rules of Logical Definition 91 

(3) An equilateral triangle is a triangle all of whose 
sides and angles are equal. 

(Equal angles is an unnecessary mark.) 
The Foregoing Definitions Made Logical. 

(1) A man is a rational biped. (Proximate genus.) 

(2) A barn is a building where horses and cattle are 
kept and hay and grain are stored. 

(3) An equilateral triangle is a triangle all of whose 
sides are equal. 

Third Rule. 

A definition must not repeat the name to be defined nor 
contain any synonym of it. 

A violation of this rule is known as "a circle in de- 
fining" ( cir cuius in definiendo ) . 

There are some exceptions to this rule, as in the 
case of compound words and a species which takes its 
name from its proximate genus. To say that a hobby- 
horse is a horse, or that an equilateral triangle is a tri- 
angle, is not only allowable but necessary, that the proxi- 
mate genus may be used. 

The follozving definitions are illogical according to the 
third rule: 

( 1 ) A teacher is one who teaches. 

(2) Life is the sum of the vital functions. 

(3) A sensation is that which comes to the mind 
through the senses. 

Fourth Rule. 

A definition must not be expressed in obscure, figurative 
or ambiguous language. 



92 Definition 

A violation of this rule is referred to in logic as "defin- 
ing the unknown by the still more unknown" (ignotum 
per ignotius). 

It is known that the purpose of definition is to make 
clear some obscure term, consequently unless every word 
used is understood the chief aim of the definition has been 
defeated. 

From this it must not be inferred that all definitions 
should be free from technical terms. Such a restriction 
would make the defining of many terms unsatisfactory 
and in a few cases practically impossible. To the student 
of evolution the following definition by Spencer is intel- 
ligible, while to the uninitiated it would appear obscure : 
"Evolution is a continuous change from an indefinite, 
incoherent homogeneity to a definite coherent heterogene- 
ity through successive differentiations and integrations. " 

This rule insists upon simple language when it is pos- 
sible to use such in giving an accurate and comprehensive 
meaning to the term defined. 
Illogical Definitions According to the Fourth Rule. 

(i) "A net is something which is reticulated and 
decussated, with interstices between the intersections." 
Dr. Johnson. 

(2) "Thought is only a cognition of the necessary 
relations of our concepts." 

(3) "The soul is the entelechy, or first form of an 
organized body which has potential life." Aristotle. 

Fifth Rule. 

When possible the definition must be affirmative rather 
than negative. 



The Rules of Logical Definition 93 

The fact that there are a considerable number of terms 
which admit of a negative definition only, takes from the 
force of this rule. Such terms as deafness, inexpressible, 
infidel and the like can best be defined negatively. 

It likewise happens that when words are used in pairs 
it is expedient to define one affirmatively and the other 
negatively. Recall, for example, the definitions of rela- 
tive and absolute terms : "A relative term is one which 
needs another term to make its meaning clear." "An 
absolute term is one which does not need another term to 
make its meaning clear." 
Illogical Definitions According to the Fifth Rule. 

(1) A gentleman is a man who is not rude. 

(2) An element is a substance which is not a com- 
pound. 

(3) An univocal term is a term which does not have 
more than one meaning. 

8. TERMS WHICH CANNOT BE DEFINED LOGICALLY. 

A logical definition insists upon a proximate genus and 
differentia. But as there is no genus higher than the 
highest genus (summum genus) then surely such cannot 
be defined logically. The words being and thing illus- 
trate terms of this class. Moreover, it is impossible to 
give a satisfactory definition of an individual (infima 
species) as no attributes can be mentioned which will dis- 
tinguish definitely and permanently the individual from 
others of the class. We may perceive the attributes but 
not those that are possessed solely by the individual. To 
say that Abraham Lincoln was a man who was simple 



94 Definition 

and honest is not a definition, as other men have had the 
same characteristics. 

Again there are a few terms such as life, death, time 
and space which cannot be defined satisfactorily. These 
terms seem to be in a class by themselves or of their own 
genus (sui generis). 

Since a definition of a term is a brief explanation of 
it by means of its attributes, it follows that collective 
terms and terms standing for a single attribute are in- 
capable of definition. Such terms as group, pain, attri- 
bute, belong to this class. 

We may say, then, that there are some terms too high, 
some too low and some too peculiar to come within the 
province of logical definition. In short, "summum genus," 
"infima species" and "sui generis" are incapable of defi- 
nition. 

9. DEFINITIONS OF COMMON EDUCATIONAL TERMS. 

(i) Development is the process whereby the latent 
possibilities of an individual are unfolded or the invisible 
conditions of a situation are made apparent. 

Development means expansion according to principle, 
while unfolding may or may not involve a principle. 

(2) Education is the process employed in developing 
systematically, symmetrically and progressively all of the 
capabilities of a single life ; or 

(3) Education is the process of modifying experience 
in order to make the life as valuable as it ought to be. 

(4) Teaching is the art of occasioning those activities 
which result in knowledge, power and skill. 



Definitions of Common Educational Terms 95 

It is the duty of the true teacher to inspire the child to 
activity along right lines. Through his own activity the 
child shapes his inner world which is sometimes termed 
character. 

Knowledge is anything known, power is ability to act. 
skill is a readiness of action. 

(5) Instruction is the art of occasioning those activi- 
ties which result in knowledge. 

Instruction develops the understanding; teaching de- 
velops character. 

(6) Training is the occasioning of those activities 
which, by means of directed exercise, result in power and 
skill. 

Training and education are not interchangeable. Train- 
ing implies an outside authority, while education, which 
involves inner development, may proceed without super- 
vision. 

(7) Knowledge is anything acquired by the act of 
knowing. 

(8) Learning is the act of acquiring knowledge or skill. 

(9) Instruction, training, teaching, learning and edu- 
cation all involve activity. 

Instruction arouses activity which results in knowledge ; 
training directs activity which produces power and skill ; 
teaching includes both instruction and training. Learning 
is an activity which results in knowledge and skill, while 
education is a developing process which involves all the 
others. 

(10) A science is knowledge classified for the pur- 
pose of discovering general truths. 



g6 Definition 

( 1 1 ) An art is a skillful application of knowledge and 
power to practice. 

"A science teaches us to know, an art to do." 

(12) A fact is a single, individual, particular thing 
made or done. 

A truth is general knowledge which exactly conforms 
to the facts. 

A truth may be a definition, rule, law, or principle. 

(13) A fact as opposed to hypothesis is an occurrence 
which is true beyond doubt. 

An hypothesis is a supposition advanced to explain an 
occurrence or a group of occurrences. 

A theory is a general hypothesis which has been partly 
verified. 

(14) Theory as opposed to practice means general 
knowledge, while practice involves the putting into opera- 
tion one's theories. 

(15) A fact as opposed to phenomenon is something 
accomplished. A phenomenon is something shown. 

(16) A method-whole is any subdivision of the mat- 
ter for instruction which leads to a generalization. 

(17) Method is an orderly procedure according to a 
recognized system of rules and principles. 

As the term is commonly used it includes not only the 
arrangement of the subject matter for instruction but 
the mode of presenting the same to the mind. 

(18) Induction is the process of proceeding from the 
less general to the more general. 

Deduction is the process of proceeding from the more 
general to the less general. 



Definitions of Common Educational Terms 97 

(19) The terms induction and deduction may have 
reference to forms of reasoning or to methods of teach- 
ing. 

The inductive method is the method of deriving a gen- 
eral truth from individual instances. 

The deductive method is the method of applying a 
general truth to individual instances. 

The inductive method is objective, while the deductive 
method is subjective. Induction is the method of dis- 
covery; deduction is the method of instruction. 

(20) Analysis is the process of separating a whole 
into its related parts. 

Synthesis is the process of uniting the related parts to 
form the whole. 

(21) The analytic method is the method of proceed- 
ing from the whole to the related parts. 

The synthetic method is the method of proceeding from 
the related parts to the completed whole. 

(22) Analysis and synthesis deal with single things, 
while induction and deduction are concerned with classes 
of things. 

(23) The complete method consists of three elements : 
(1) induction, (2) deduction, (3) verification or proof. 

When the emphasis is placed on the inductive phase, 
the complete method is sometimes termed the develop- 
ment method. 

10. OUTLINE. 

Definition. 

(1) Importance. 



98 Definition 

(2) The Predicables. 

Genus — species — summum genus — infima species. 
Proximate Genus. 

Genus and Species of Natural History. 
Genus, Double meaning of 

Differentia. 

Property. 

Accident. 

Separable, Inseparable. 

(3) Nature of Definition. 

(4) Definition and Division Compared. 

(5) The Kinds of Definitions. 

(1) Etymological. 

(2) Descriptive. 

(3) Logical. 

Three Kinds Illustrated and Compared. 

(6) When the Three Kinds are Serviceable. 

(7) The Rules of Logical Definition. 

(1) Essentials. 

(2) Same size. 

(3) Do not repeat. 

(4) Unambiguous. 

(5) Language affirmative. 

(8) Terms Which Cannot be Defined Logically. 

Summum genus. 
Infima species. 
Sui generis. 
Collective terms. 
A single attribute. 

11. SUMMARY. 

(1) To be logical one must acquire the habit of accurate 
definition. 

This topic ought to appeal strongly to the school teacher, who 
should above all others make his work stand for clearness, 
pointedness and continuity. 

(2) A predicable is a term which can be affirmed or predi- 
cated of any subject. 



Summary 99 

The five predicables are Genus, Species, Differentia, Property 
and Accident 

(1) A Genus is a term which stands for two or more sub- 

ordinate classes. 

(2) A Species is a term which represents one of the sub- 

ordinate classes. 

The proximate genus of a species is the next class above 
the species, while the summum genus is the highest pos- 
sible class in any graded series of terms. The lowest 
class is the infima species of that series. The lowest 
class may be individual. 

In natural history genus and species are not relative 
terms, but absolute, having a fixed place in the series 
of gradations. 

The term genus possesses a double meaning: it may be 
used to represent objects (extensionally) or qualities 
(intensionally). 

(3) The differentia is that attribute which distinguishes a 

given species from all the other species of the genus. 

(4) A property of a term is any attribute which helps to 

make that term what it is. 
Differentia is a property according to definition. Some 
logicians would not include the differentia in the content 
of the term property. 

(5) An accident of a term is any attribute which does not 

help to make it what it is. Some authorities divide 
accidents into separable and inseparable. 

(3) A definition of a term is a statement of its meaning by 
enumerating its characteristic attributes. 

(4) Definitions explain a term intensionally, while logical 
division explains a term extensionally. 

(5) There are three kinds of definitions: (1) etymological, 
(2) descriptive, (3) logical. 

An etymological definition is based upon the derivation of the 
term; a descriptive definition states the characteristic properties 
and accidents of a term, while a logical definition is simply a 
statement of the differentia of a term. 



ioo Definition 

(6) The etymological definition leads to precision of expres- 
sion, the descriptive definition is best adapted to the child-mind, 
while the logical definition belongs to the realm of secondary 
education. 

(7) Five rules summarize the requirements to which a logical 
definition must conform. In a word or two these five rules are: 
Every logical definition must (1) state the genus and differentia, 
(2) be equivalent to the species defined, (3) not repeat the name 
to be defined, (4) not be expressed in obscure language, (5) 
commonly be affirmative. 

(8) Some terms are too high (summum genus), some too 
low (infima species), some too peculiar (sui generis) to come 
within the province of logical definition. 

12. ILLUSTRATIVE EXERCISES. 

la. The italicized words in the following propositions are 
predicables because they are affirmed of the subject: 

(1) "This man weighs one hundred fifty pounds." 

(2) "A bird is a feathered biped." 

(3) "The earnest teacher is an indefatigable worker." 

(4) "Walking is the most beneficial outdoor exercise." 

lb. Underscore the predicables in the following : 

(1) "All men are rational." 

(2) "Teachers must be just." 

(3) "Every form of unhappiness springs from a wrong con- 

dition of the mind." 

(4) "Calmness of mind is one of the beautiful jewels of 

wisdom." 
2a. To clarify our ideas it is an excellent plan to select a 
group of words belonging to the same genus with a view of de- 
fining them as simply and expeditiously as possible. As an illus- 
tration building may be selected as a genus. The word kind will 
suggest to us the species, such as dwelling, church, theatre, 
school, barn, bird-house, granary and smoke-house. Next it is 
necessary to discover the basis of distinction. This seems to be 
the use to which the building is put. Now we are ready for the 
definitions : 



Illustrative Exercises 



101 



Species 


Genus 


Differentia 


A dwelling is 


a building 


where people live. 


" church 


U <( 


where people worship. 


" theatre 


(( it 


where people act. 


" school 


a a 


where children are taught. 


" barn 


a <« 


where domestic animals, hay 
and grain are kept. 


" bird-house " 


n a 


designed for birds. 


" granary 


(t (C 


where grain is stored. 


" smoke-house " 


a a 


where meat is smoked. 



2b. By selecting man as the genus, define the terms Caucasian, 
Mongolian, Ethiopian, Malay and American Indian. Treat the 
term chair in the same manner. 

3a. One may easily distinguish a property from an accident 
by asking himself the question, "Would subtracting the attribute 
from the term alter its identity"? For example in the following, 
I find that the words italicized are properties because subtracting 
each from the term changes its identity : 
Term • Attributes 

man age, rationality, possessions, 

book binding, leaves, size, color, contents, 

radium emits intense light and heat, costs a million dol- 
lars a pound, 
snail . air-breathing mollusk, moves slowly, 

slush soft mud and snow, six inches deep. 

3b. Indicate the common attributes of the following terms, 
underscoring the properties : Tree, teacher, garden, house, river. 
4. The rules summarize well the essentials of the subject mat- 
ter of the logical definition. Therefore, it is highly important 
for the student to have these rules at the "tip of the tongue." 
With this in view a device of this nature may be helpful. Make 
each letter of the word rules stand for the initial letter of a sug- 
gestive word in each of the five rules. For example: r (repeat), 
u (unambiguous), 1 (language affirmative), e (essential), s (same 
size). 

With a little study "r and repeat," "u and unambiguous," "1 and 
language affirmative," "e and essential," "s and same size" may be 
firmly linked together in the memory. Repeat suggests the third 
rule, do not repeat the name, etc.; unambiguous, the fourth rule, 



102 Definition 

not ambiguous language, etc.; language affirmative, the fifth rule; 
essentials, the first rule; same size, the second rule, subject and 
predicate must be of same size. The fact that the rules are not 
recalled in order of treatment is inconsequential. 

It is the writer's experience that fifteen minutes of concen- 
trated study upon this device or one similar to it will indelibly 
stamp upon the mind these troublesome rules. 

The student may be able to devise a more helpful keyword. 

13. REVIEW QUESTIONS. 

(1) Why should the subject of definition appeal strongly to 
the school teacher? 

(2) Define a predicable. 

(3) Name in order the five predicables. 

(4) Define and illustrate the terms genus and species. 

(5) Explain the terms summum genus, infima species, sui 
generis. 

(6) Illustrate proximate genus. 

(7) Explain the terms genus and species as used in natural 
history. 

(8) Exemplify the double meaning of the genus man. 

(9) Define and illustrate differentia. 

(10) In what sense is the species a richer term than the genus? 

(11) Distinguish between property and accident. 

(12) Illustrate separable and inseparable accidents. 

(13) Give descriptive definitions of the following, indicating 
the five predicables : logic, general term, non-connotative term, 
obversion. 

(14) Define definition; illustrate. 

(15) Distinguish between definition and division. 

(16) Name, define and illustrate the three kinds of definitions. 

(17) Distinguish between real and verbal definitions. 

(18) Define in three ways the following: king, government, 
city, metal. 

(19) State the rules of logical definition. 

(20) What words may be used as cues to aid in recalling 
the rules for logical definition? 

(21) Under what circumstances will the wise teacher make 
use of each of three kinds of definitions? 



Review Questions 103 

(22) Relative to the second rule for logical definition what 
are the three questions that one should ask himself? 

(23) Explain the exceptions to the third rule. 

(24) In connection with the fourth rule what may be said as 
to the use of technical terms? 

(25) What facts take from the force of the fifth rule? 

(26) What classes of words do not admit of logical definition? 
Illustrate. 

(27) Define education, teaching, instruction, training. 

(28) Distinguish by illustration between induction and syn- 
thesis ; deduction and analysis. 

14. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Why should the scholar be tempted to speak and write 
illogically ? 

(2) Name the parts of speech that may be classed as pred- 
icables. 

(3) Explain the ten categories as given by Aristotle. 

(4) Show that genus and species are relative terms. 

(5) Why should the definition be needed most in the abstract 
sciences, such as theology, ethics, political economy, juris-pru- 
dence and psychology? 

(6) Define sin, life, wrong, personality, habit, character. 

(7) From the viewpoint of natural history find the species in 
the series of terms of which polygon is a member. 

(8) What is the plural of differentia? 

(9) Why should logic insist upon the proximate genus ? 

(10) (a) Man is a rational animal. 

(b) Man is a rational biped (proximate genus). 
In the case of the immature mind the first definition would be 
clearer. Why ? 

(11) "A property of a term is any mark or characteristic which 
belongs to that term." Is this definition logical? Give reasons. 

(12) What is the difference between the logical and the popular 
conception of property? 

(13) Is there any difference between the logical and popular 
conception of accidents? 

(14) "The term confer entia might be used to stand for the 



104 Definition 

essence of the genus, as the term differentia represents the es- 
sence of the species." 1 Explain this. 

(15) John Stuart Mill affirms that there is no such thing as a 
real definition. Discuss this. 

(16) In your opinion, of the five rules of logical definition 
what one is violated most by the average teacher? Give reasons. 

(17) Distinguish between symbol and content. 

(18) Why are descriptive definitions best for young children? 
What educational principle is involved? 

(19) From the standpoint of the five rules for logical defini- 
tion criticise the following: 

(1) A man is a reasonable vertebrate. 

(2) A gentleman is a man with no visible means of 

support. 

(3) A man is an organized entity whose cognitive powers 

function rationally. 

(4) A metal is an element with a metallic luster. 

(5) A triangle is a figure of three sides. 

(6) A teacher is one who imparts knowledge. 

(7) Education is the process of drawing out all that is 

beautiful in the body and noble in the soul. 

(8) A democrat is a man who believes in free trade. 

(9) A government is a commonwealth controlled by di- 

rect vote of the people. 

(20) Write the foregoing definitions in logical form. 

(21) Since man is the only animal given to laughter, why is 
not the following a logical definition : "Man is a laughing animal." 

(22) "A logical definition should contain the species, the genus 
and the appropriate differentia." Is there any reason for using 
the term appropriate? 

(23) In connection with genus and species explain subaltern. 

(24) Is laughter a property of human being or an accident? 

(25) Show how a pedagogue may be an instructor but not a 
teacher. 

(26) Illustrate the complete method. 

(27) Show that induction may consist of a series of analyses; 
also a series of syntheses. 



l Hyslop. 



CHAPTER 7. 

LOGICAL DIVISION AND CLASSIFICATION. 

1. NATURE OF LOGICAL DIVISION. 

The term genus is used for any class name which 
stands for two or more subordinate classes while the 
term species is made to stand for any one of the sub- 
ordinate classes. 

The proximate genus of any species is the next class 
above. For example the proximate genus of man is 
biped, not animal. 

Logical division is the process of separating a proximate 
genus into its co-ordinate species. 



Illustrations : 
Genus 



(i) Heavenly bodies 



(2) Vertebrates 



Species 

Fixed stars 

Planets 

Satellites 

Comets 

Meteors 

Nebulae 

Leptocardians 

Fishes 

Amphibians 

Reptiles 

Birds 

Mammals 



105 



io6 



Logical Division and Classification 



(3) Man 



(4) Government 



Caucasian 
Mongolian 
Malay 
Ethiopian 
American Indian 

Monarchy 

Aristocracy 

Democracy 



2. LOGICAL DIVISION DISTINGUISHED FROM ENUMERA- 
TION. 

When the genus is separated at once into individual 
objects the process is not logical division, but simple 
enumeration. Logical division implies a separating into 
smaller class terms, each term being a genus of still 
smaller subdivisions. This process may be continued till 
the last division gives individuals as species. Enumera- 
tion takes place when the first subdivision results in a list 
of individuals. To illustrate: 



Teacher 



Logical Division. 

Science teacher 
Mathematics teacher 

J English teacher 

I Modern language teacher 



Enumeration. 



Teacher 



John J. Brown 
H. G. White 
Mary Jones 
Alice Smith 



.ogical Division as Partition 



10: 



3. LOGICAL DIVISION AS PARTITION. 

Partition is the process of separating an individual 
thing into its parts. 

The partition is quantitative or mathematical when the 
separation is in terms of space or time, but when other- 
wise the partition becomes qualitative or logical. Or to 
put it in another way, the partition is mathematical when 
the separation gives parts and logical when the separation 
gives ingredients. 

To illustrate: 



( i ) Tree- 



(2) House- 1 



quantitative 

or 
(mathematical) 

qualitative 

or 
(logical) 

quantitative 

or 
(mathematical) 



branches 

leaves 

roots 

trunk 

Voody fibre 

capillary attraction 

sap 

chlorophyll 

[roof 

1 frame-work 

[foundation 

wood 
iron 
stone 
plaster 



qualitative 

or 
(logical) 

An easy way to determine that the separation involves 
logical division proper and not partition is to affirm the 
connection between a class and a sub-class. To wit: A 
man is a biped ; a square is a rectangle ; a Caucasian is a 



108 Logical Division and Classification 

man, etc. If such an affirmation cannot be made then 
the separation involved is not properly logical division 
but probably partition. For example it cannot be said 
that a roof is a house, or that sap is a tree. It is seen, 
then, that a logical division of any genus may be sum- 
marized in the form of a series of judgments of which a 
species is the subject and the genus is the predicate. For 
example, by a logical division quadrilaterals may be di- 
vided into trapeziums, trapezoids and parallelograms; 
this process may then be summarized in a series of three 
judgments: (i) A trapezium is a quadrilateral; (2) A 
trapezoid is a quadrilateral; (3) A parallelogram is a 
quadrilateral. 

4. RULES OF LOGICAL DIVISION. 

When the logical division of a genus is under consider- 
ation there are four rules which should be observed. 

First Rule. There must be but one principle of divi- 
sion (fundamentum divisionis). To divide mankind into 
white man, Australian, yellow man, African and red 
man is a violation of this rule as the two principles of 
color and geographical location are involved. A division 
in which more than one principle is used is sometimes 
referred to as cross division because the various species 
cross each other. For example in the foregoing there 
are many white men who are Australians. 

This rule applies only to one division. Where there 
is a series of divisions a new principle may be employed 
in each division. For example, in dividing triangles into 
scalene, isosceles and equilateral, the equality of sides is 



Rules of Logical Division 109 

the principle involved, but, in subdividing isosceles tri- 
angles into right angled and oblique angled, the principle 
employed concerns the nature of the angle. 

Second Rule. The co-ordinate species must be mu- 
tually exclusive. There must be no overlapping. The il- 
lustration given in the first rule is likewise a violation of 
this rule. Another example in which this second rule is 
not obeyed may be found in most geometries where tri- 
angles are divided into scalene, isosceles and equilateral. 
Here the second and third classes are not mutually ex- 
clusive since all equilateral triangles are isosceles accord- 
ing to the usual definition, "An isosceles triangle is a 
triangle having two equal sides." All equilateral triangles 
have two equal sides. 

Third Rule. The division must be exhaustive. That 
is, the species taken together must equal the whole genus. 
The sum of the species must be co-extensive with the 
genus. 

Dividing man into Caucasian, Ethiopian and Mongolian 
would be a violation of this rule, as there are at least two 
other species of man, Malay and American Indian. 

A distinction should be made between an exhaustive 
division and a complete division as the latter is not a 
logical requirement. To divide government into mon- 
archy, aristocracy and democracy is exhaustive but in- 
complete. Exhaustive because there is no other kind of 
government, all the species are included ; but incomplete 
in that monarchy may be divided into absolute and 
limited; democracy into pure and representative. 

Fourth Rule. The division must proceed from the 



no Logical Division and Classification 

proximate genus to the immediate species. There should 
be no sudden jumps from a high genus to a low species. 
The division must be gradual and continuous; step by- 
step. To divide government into limited monarchy, abso- 
lute monarchy, pure democracy and representative de- 
mocracy would be a violation of this rule, as government 
is the proximate genus of monarchy, not of limited mon- 
archy, therefore one step has been omitted. Such an omis- 
sion involves a step from grandfather to grandchild, 
so to speak, the generation of father having been left 
out. 

A violation of this rule is most insidious when some of 
the species of a subdivision are immediate while others 
are not. To wit : dividing government into monarchy, 
aristocracy, pure democracy and republic, or dividing 
quadrilaterals into trapeziums, trapezoids, rectangles, 
squares, rhomboids and rhombs. 

5. DICHOTOMY. 

Dichotomy comes from the Greek, meaning to cut in 
two. Dichotomy is a continual division of a genus into 
two species which are contradictory in nature. 

Contradictory terms are such as admit of no middle 
ground. They divide the whole universe of thought into 
two classes. For example, honest and not-honest, pure and 
impure, perfect and imperfect, are contradictory terms. 
Dichotomy thus affords an easy opportunity for an ex- 
haustive division as in the use of contradictories nothing 
in the universe need be omitted. 

An historical illustration of dichotomy is the "Tree of 



Dichotomy 



in 



Porphyry" named after Porphyrius, a Neo-Platonic 
philosopher of the third century. 

Tree of Porphyry. 
Substance. 



Corporeal Incorporeal 



Body 



Animate Inanimate 



Living Being 



Sensible Insensible 



Animal 



Rational Irrational 



Man 



Socrates Plato Other Men 



H2 Logical Division and Classification 

This kind of division is not altogether satisfactory as 
the negative side is too indefinite. On the other hand, if 
both subdivisions are made positive then there is danger 
of making the opposing terms contrary rather than con- 
tradictory. This, of course, would be a serious logical 
fallacy, as contrary terms admit of middle ground while 
contradictory terms give no choice, it is either the one or 
the other. 

The use of dichotomy becomes evident in situations 
where new and unexpected discoveries may be made. 
Without disturbing the classification the new species may 
be appended to the negative side of the division. The 
following illustrates : 

Vertebrates 

i ' 1 

Leptocardians Not-leptocardians 

Fish Not-Fish 



I ' — l 

Amphibians Not-amphibians 



1 ' 1 . 

Reptiles Not-reptiles 

i 



Birds Not-birds 



•'-— 1 



Mammals Not-mammals 

I 

The New Species 

6. CLASSIFICATION— COMPARED WITH DIVISION. 

Classification is the process of grouping notions ac- 
cording to their resemblances or connections. 

So far as results are concerned there is no difference 



Classification — Compared with Division 113 

between logical division and classification. Both processes 
may give us the same orderly scheme of heads and sub- 
heads. The difference lies in the process itself. Division 
is deductive in nature as it proceeds from the more gen- 
eral genus to the less general species. While classifica- 
tion is inductive as it groups the less general species under 
the more general genus. Division differentiates unity 
into multiplicity, while classification reduces multiplicity 
to unity. It follows that the one is the inverse of the 
other. The difference in the mode of procedure may be 
illustrated by using the common classification or division 
of triangles. For example : 

Without any knowledge of the kinds of triangles the 
student discovers by examining the various shapes of 
many triangles that there is a group in which none of the 
sides are equal. For the lack of a better name he terms 
these non-equilateral (scalene). Further observation dis- 
closes another group in which two of the sides are equal. 
These he names bi-equilateral (isosceles). Finally a 
third group is designated as tri-equilateral (equilateral). 
This process is classification. Division would consist in 
separating the genus triangle into the three kinds — 
scalene, isosceles, equilateral. 

7. KINDS OF CLASSIFICATION— ARTIFICIAL AND 
NATURAL. 

An artificial classification is one in which the grouping 
is made on the basis of some arbitrary connection. Cata- 
loguing alphabetically the books in a library illustrates 
this kind of classification. Likewise the arrangement of 



H4 Logical Division and Classification 

the names in a directory or a telephone book. The con- 
necting mark being the initial letter of the title or name. 
The reason why Mills and Meyers are put in the same 
group is that both names happen to commence with the 
letter M. 

Artificial classifications are resorted to for some special 
purpose, designed by man, not by nature. Consequently 
artificial classifications are sometimes called special or 
working classifications. 

A natural classification is one in which the grouping is 
made on the basis of some inherent mark of resemblance. 

Classifications in animal and plant life are the best il- 
lustrations of this kind. Such classifications are sug- 
gested by nature and not by man, and may, therefore, be 
called general or scientific. The main aim of natural 
classification is to derive general truths and arrange 
knowledge so that it may be easily remembered. 

8. TWO RULES OF CLASSIFICATION. 

The rules of logical division are applicable in the mak- 
ing of a logical classification. In addition to these an 
artificial classification should be made to conform to the 
one rule: The classification must be appropriate to the 
purpose in hand. Likewise a natural classification should 
be made to conform to the rule: Every classification 
should afford opportunity for the greatest possible num- 
ber of general assertions. 

9. USE OF DIVISION AND CLASSIFICATION IN THE 

SCHOOL ROOM. 

It has been stated that classification and division aim 



Use of Classification and Division 115 

at the same result. Classification reduces multiplicity to 
unity while division differentiates unity into multiplicity. 
In short, division is deductive while classification is 
inductive in mode of procedure. Therefore, classification 
should be used in those situations which call for induc- 
tion and division in cases where deduction is the better 
method. 

Speaking generally, classification should be used with 
small children when the essential thing is to present the 
concrete facts with a view of leading the children to dis- 
cover for themselves the truths contained therein. 

With older pupils division may be used, if the purpose 
is to set in order facts which are already known. 

10. TOPICAL OUTLINE. 

Logical Division and Classification. 

(1) Nature of Logical Division. 

Genus — species. 
Illustrations. 

(2) Logical Division Distinguished from Enumeration. 

Illustrations. 

(3) Logical Division and Partition. 

Quantitative — qualitative. 
How summarized. 

(4) Four Rules of Logical Division. 

(1) One principle — cross division. 

(2) Mutually exclusive. 

(3) Exhaustive — complete. 

(4) Immediate species. 

(5) Dichotomy. 

Contradictory terms. 
Tree of Porphyry. 
Use illustrated. 



n6 Logical Division and Classification 

(6) Classification Compared with Division. 

(7) Kinds. Artificial— Natural. 

(8) Two Rules of Classification. 

(1) Appropriate, (2) Afford many Assertions. 

(9) Use of Division and Classification. 

11. SUMMARY. 

(1) Logical division is the process of separating a proximate 
genus into its co-ordinate species. 

(2) The first subdivision in a logical division gives class 
terms, while the first subdivision in an enumeration gives indi- 
vidual objects. 

(3) Partition is the process of separating an individual thing 
into its parts. These parts may be either quantitative or 
qualitative. 

A logical division of any genus may be summarized in a series 
of judgments of which a species is the subject and the genus is 
the predicate. 

(4) The four rules of logical division are: the division must 
(1) be based on one principle, (2) have species mutually ex- 
clusive, (3) be exhaustive and (4) proceed from proximate genus 
to immediate species. 

A violation of the first rule gives a cross division. 
Exhaustive division is easily confused with a complete or 
finished division. 

(5) Dichotomy is a continual division of a genus into two 
species which are contradictory in nature. 

An historical illustration of dichotomy is the Tree of Porphyry. 
Dichotomy is of service in the field of new and unexpected 
discoveries. 

(6) Classification is the process of grouping notions accord- 
ing to their resemblances or connections. 

Classification is inductive in nature, division deductive. Classi- 
fication unifies, division differentiates. 

(7) An artificial classification is made on the basis of some 
arbitrary connection; a natural classification, on some inherent 
mark of resemblance. 

(8) The rules of logical division are applicable in any classi- 
fication. In addition to these a classification should (1) be ap- 



Summary 



117 



propriate and (2) afford opportunity for the greatest possible 
number of assertions. 

(9) Classification should be the mode of procedure in the 
lower grades, division in the higher grades. 



12. REVIEW QUESTIONS. 

(1) Define and illustrate logical division. 

(2) What is the meaning of proximate genus ? 

(3) How does logical division differ from enumeration? 
Illustrate. 

(4) Distinguish between logical division, and physical division 
or partition. 

(5) Illustrate a quantitative partition; a qualitative partition. 

(6) Illustrate how a logical division may be summarized in 
the form of a series of judgments. 

(7) State and explain the rules of logical division. 

(8) State the rules violated in the following divisions, 



explaining in full 










'Primary 






Secondary 




r In fancy 




Collegiate 




Childhood 


(1) Education 


Technical 


(2) Life 


Youth 




Scientific 




Old age 




Professional 






Caucasian 




Cement 
Frame 




Ethiopian 




Stone 


(3) Man - 


Malay 
Mongolian 


(4) Buildings 


Dwellings 
Barns 




American 




Churches 



(9) Show the difference between contradictory and opposite 
terms. 

(10) Define dichotomy. 

(11) Illustrate the Tree of Porphyry and indicate its use to 
scientists. 

(12) Illustrate the difference between classification and division. 

(13) Why should classification be the mode of procedure when 
dealing with immature minds ? 



n8 Logical Division and Classification 

(14) Illustrate the difference between an artificial and a natural 
classification. 

(15) State and explain the two rules of classification. 

(16) Show which of the following divisions are logical and 
which are not : 

(1) The manifestations of the mind into knowing, think- 

ing and feeling. 

(2) Books into mathematical and non-mathematical. 

(3) Students into those who are industrious, athletic and 

shiftless. 

(4) Flowers into roses, carnations and lilies. 

(5) Planets into those which are larger than the earth 

and those which are smaller. 

13. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Analyze by mathematical partition the terms world, plant, 
book. 

(2) Analyze by logical partition the terms granite, water, air. 

(3) What rule is violated if the logical division is applied to 
the genus rather than the proximate genus ? 

(4) Divide logically the following terms : school, religion, 
book, vegetable, life. 

(5) "Each new subdivision may adopt a new principle of divi- 
sion." Illustrate this. 

(6) Explain and illustrate the meaning of the terms super- 
ordinate, sub-ordinate and co-ordinate. 

(7) Define and illustrate metaphysical division and verbal 
division. 

(8) Give a definition of an isosceles triangle which will make 
logical the division of triangles into scalene, isosceles and equi- 
lateral. 

(9) "The evolution of all truth develops progressively through 
three stages." "The first is the thesis ; the second is the antithesis ; 
the third is the synthesis." Explain this in terms of trichotomy. 

(10) Illustrate the difference between a complete division and 
an exhaustive division. 



Questions for Original Thought 



119 



(11) Show in what ways, if any, the following divisions violate 
the rules of logical division. 



Human Learning 
(by Bacon) 



Memory 

(History) 
Imagination 

(Poetry) 
Reason 
(Philosophy) 

or 
(the Sciences) 



Sciences 
(by Comte) 



1 Mathematics 

2 Astronomy 

3 Physics 

4 Chemistry 

5 Biology 

6 Sociology 

7 Morals 



CHAPTER 8. 



LOGICAL PROPOSITIONS 



1. THE NATURE OF LOGICAL PROPOSITIONS. 

Judging has been defined as the process of conjoining 
or disjoining notions. This may be put in another way: 
"Judging is the process of asserting or denying the agree- 
ment between two notions." The product of the act of 
judging is a judgment and when judgments are put in 
word- form such expressions are called logical propositions. 

Definition: A logical proposition is a judgment ex- 
pressed in words. Just as percept and concept notions 
are expressed by means of logical terms so judgment 
notions may be expressed by logical propositions. 

To illustrate : The terms the squirrel and cracking a nut 
express two notions, and when an agreement between 
them is asserted and the product is expressed in word 
form, then such an expression becomes the logical propo- 
sition, "The squirrel is cracking a nut." 

The following being expressed judgments are logical 
propositions : 

(i) All men are mortal. 

(2) Some men are wise. 

(3) No men are immortal. 

(4) Some men are not wise. 

(5) No sane person is a lover of vice. 

(6) Some good orators are not good statesmen. 

(7) Every man is fallible. 

120 



The Nature of Logical Propositions 121 

(8) If it rains, I shall not go. 

(9) He is either sane or insane. 

2. KINDS OF LOGICAL PROPOSITIONS. 

There are three kinds of logical propositions; namely, 
categorical, hypothetical and disjunctive. 

A categorical proposition is one in which the assertion 
is made unconditionally. An hypothetical proposition is 
one in which the assertion depends upon a condition. A 
disjunctive proposition is one which asserts an alternative. 

The Three Kinds Illustrated : 

( 1 ) "Every dog has his day." Categorical. 

(2) "If you do your best, success will reward you." 

Hypothetical. 

(3) "He is either stupid or indolent." Dis- 

junctive. 

(4) "All vices are reprehensible." Categorical. 

(5) "Either you are very talented or very indus- 

trious." Disjunctive. 

(6) "If capital punishment does not aid society, 

it should be abolished." Hypothetical. 

(7) "You may go provided your teacher is will- 

ing." Hypothetical. 

(8) "No intelligent man can ignore the practice 

of temperance." Categorical. 
By studying the illustrations it will be observed that the 
categorical propositions are direct, bold, assertive state- 
ments, whereas the hypothetical are limited by conditions 
which make them less forceful. In the second proposi- 
tion, for example, "success will reward you," is limited 



122 Logical Propositions 

by the condition, "If you do your best." The disjunctive 
may be regarded as categorical in form, but hypothetical 
in meaning, because in such a proposition as, "He is either, 
stupid or indolent," a direct assertion is made which sug- 
gests the categorical, and yet it may be implied that, if 
he is stupid then he is not indolent; this is indicative of 
the hypothetical. 

Some logicians classify propositions as categorical and 
conditional, the conditional being subdivided into hypo- 
thetical and disjunctive. The first classification seems 
preferable, however, as it conforms to the three modes of 
reasoning. 

The common word-signs of the categorical proposition 
are all, every, each, any, no and some, while those of the 
hypothetical are if, even if, unless, although, though, pro- 
vided that, when, or any word or group of words denoting 
a condition. The disjunctive symbols are either — or. 

3. THE FOUR ELEMENTS OF A CATEGORICAL PROPO- 
SITION. 

Every categorical proposition should have four ele- 
ments; namely, the quantity sign, the logical subject, the 
copula and the logical predicate. In the foregoing cate- 
gorical propositions the quantity signs are respectively, 
every, all and no. In any case the quantity sign is 
always attached to the subject and indicates its breadth 
or extension. For example, in the two propositions, "All 
men are mortal" and "Some men are wise," the quantity 
sign all makes the term man much broader than does the 
quantity sign some. 



The Four Elements of a Categorical Proposition 123 

The logical subject of a categorical proposition is the 
term of which something is affirmed or denied, whereas 
the logical predicate of a categorical proposition is the 
term which is affirmed or denied of the subject. In the 
two propositions, "All men are mortal" and "No men are 
immortal," the term about which something is affirmed 
or denied is men, while the terms which are affirmed and 
denied of the subject are respectively mortal and im- 
mortal. "Men" is, therefore, the logical subject of each 
proposition, while "mortal" is the logical predicate of the 
first and "immortal" the logical predicate of the second. 
The copula is the connecting word between the logical 
subject and predicate and denotes whether or not the 
latter is affirmed or denied of the former. The copula is 
always some form of "to be" or its equivalent. When 
the predicate is denied of the subject, "nof } may be used 
with the copula and considered a part of it. To illustrate : 
in the logical proposition, "Some men are not wise," "are 
not" may be regarded as the copula. 

The four elements are indicated in the following cate- 
gorical propositions : 



ntitysig 


'n Logical subject 


Copula Logical predicate 


All 


fixed stars 


are self-luminous 


No 


wise man 


is going to steal 


Some 


quadrupeds 


are domestic animals 


Some 


glittering things 


are not gold 


Some 


boys 


are not discreet 


A few 


men 


are multi-millionaires 


Every 


citizen 


is duty-bound to vote 



124 Logical Propositions 

The student must ever keep in mind the fact that to 
be absolutely logical all categorical propositions must be 
expressed in terms of the four elements. However, life 
is too short and man is too busy to speak always in terms 
of the four elements. Moreover, to be logical may often 
compel an awkwardness of expression and a lack of 
euphony which could hardly be tolerated. For these rea- 
sons the utterances in ordinary conversation are fre- 
quently illogical so far as the four elements are con- 
cerned, though not necessarily illogical in meaning. When 
it is desired to test the validity of any series of statements 
leading up to some generalization, it may become neces- 
sary to express the statement in terms of the four ele- 
ments. The student should gain some facility in this, 
otherwise he may be readily led into fallacious reasoning. 

The following statements taken at random from news- 
papers are given in the original and then expressed in 
terms of the four elements : 

The Original In Terms of the Four Elements 

(1) You came too late. (1) The person is one who 

came too late. 

(2) I saw the swell turnout (2) The man was one who saw 

coming along. the swell turnout coming 

along. 

(3) All of the men walked. (3) All of the men were those 

who walked. 

(4) The robbers cut a hole in (4) All the robbers were the 

this floor. ones who cut a hole in 

this floor. 

(5) Some of these flew away. (5) Some birds were those 

which flew away. 



The Four Elements of a Categorical Proposition 125 

(6) The rain interfered with (6) The rain was that which 

the attendance. interfered with the at- 

tendance. 

(7) Our habits make or un- (7) All our habits are forces 

make us. which make or unmake 

us. 

(8) We all had a fine time. (8) All the party were those 

who had a fine time. 

In argumentative discourse it is often sufficient to 
"think the proposition" in terms of the four elements 
without taking the time to actually express it. 

4. LOGICAL AND GRAMMATICAL SUBJECT AND PREDI- 
CATE DISTINGUISHED. 

The grammatical subject is one word while the logical 
subject is the grammatical subject with all its modifiers 
except the quantity sign. For example: in the proposi- 
tion, "All white men are Caucasians," men is the gram- 
matical subject, while white men is the logical subject. 
All being the quantity sign simply indicates the extension 
of men and is not a part of the logical subject. 

The grammatical predicate is the verb-form together 
with any predicate noun or adjective, while the logical 
predicate is the predicate word or words and all its modi- 
fiers. The grammatical predicate includes the copula, but 
the logical predicate never includes the copula. The 
grammatical predicate does not include the object, while 
the logical predicate always includes what is equivalent 
to the object and all its modifiers. To illustrate: in the 
proposition, "Some men are wise," are wise is the gram- 
matical predicate, while wise is the logical predicate. 
And in the proposition, "He burned the red house on the 



126 Logical Propositions 

hill," burned is the grammatical predicate, while the one 
who burned the red house on the hill is the logical predi- 
cate. 

5. THE FOUR KINDS OF CATEGORICAL PROPOSITIONS. 

Categorical propositions are divided according to their 
quantity into Universal and Particular and according to 
their quality into Affirmative and Negative. 

A universal proposition is one in which the predicate 
refers to the whole of the logical subject. 

Illustrations : 

(i) All men are mortal. 

(2) All civilized men cook their food. 

(3) No dogs are immortal. 

(4) Every man was once a boy. 
Considering the first proposition, "mortal'' the logical 

predicate, refers to the whole of the logical subject "men." 
Similarly "cook their food" refers to the whole of the 
term "civilized men" ; "immortal" to the whole of the 
term "dogs," and "once a boy" to the whole of the term 
"man." 

In considering the definition of a universal proposition 
it is necessary to keep in mind the distinction between a 
logical and a grammatical subject, as in the second propo- 
sition the logical predicate, "cook their food," refers to 
only a part of the grammatical subject, men, and, there- 
fore, the proposition might fallaciously be termed a par- 
ticular proposition rather than a universal. 

A particular proposition is one in which the predicate 
refers to only a part of the logical subject. 



The Four Kinds of Categorical Propositions 127 

Illustrations : 

( 1 ) Some men are wise. 

(2) Some animals are not quadrupeds. 

(3) Most elements are metals. 

(4) Many children are mischievous. 

In the foregoing propositions some, most and many are 
quantity signs and, therefore, must not be considered as 
a part of the logical subjects. Considering the logical 
subjects and predicates in order, the term wise refers to 
only a part of the men in the world, quadrupeds to only 
a part of the animals, metals to only a part of the ele- 
ments and mischievous to only a part of the children. 

An affirmative proposition is one which expresses an 
agreement between subject and predicate. 

A negative proposition is one which expresses a dis- 
agreement between subject and predicate. 

Affirmative propositions conjoin terms, negative propo- 
sitions disjoin terms. In the first the agreement is af- 
firmed; in the second the agreement is denied. 

Illustrations : 

None of the captives escaped. Negative. 

Some teachers are just. Affirmative. 

All trees grow towards heaven. Affirmative. 

Some people are not companionable. Negative. 

No person is above criticism. Negative. 

Dividing both universal and particular propositions as 

to quality, gives four kinds ; namely, universal affirmative, 

universal negative, particular affirmative and particular 

negative. No topic in logic demands greater familiarity than 



128 Logical Propositions 

these four types, as every proposition must be reduced to 
one of the four before it can be used as a basis of reasoning. 
For the sake of brevity the symbols A, E, I and O are 
used to designate respectively the universal affirmative, 
the universal negative, the particular affirmative and the 
particular negative. A and I, symbolizing the affirmative 
propositions, are the first and second vowels in Affirmo, 
while E and O, symbolizing the negatives, are the vowels 
in Nego. The common sign of the universal affirmative, 
or the A proposition is all; of the universal negative, or E 
proposition no; of the particular affirmative, or I propo- 
sition some; of the particular negative, or O proposi- 
tion some with not as a part of the copula. The accom- 
panying classification summarizes these facts, S and P being 
used to symbolize the terms "subject" and "predicate." 

Illustrations 
f Affirmative- A All S is P 
Universal «j 

„ L . , I Negative-E No S is P 

Categorical i »» » 

Propositions f Affirmative-I Some S is P 

Particular -j 

[Negative-O Some S is not P 
Henceforth the symbols A, E, I, O will be used to desig- 
nate the four kinds of categorical propositions. The 
propositions have other quantity signs aside from the ones 
used above. These may be summarized : 

A — all, every, each, any, whole. 
E — no, none, ail-not. 
<; I — some, certain, most, a few, many, 

the greatest part, any number. 
[O — some - - not, few. 



Quantity signs of 



Propositions Which do not Conform 129 

6. PROPOSITIONS WHICH DO NOT CONFORM TO THE 
LOGICAL TYPE. 

It has been observed that all expressed judgments must 
be reduced to one of the four logical types A, E, I or O, 
before they can be used argumentatively. Logic insists 
upon definiteness and clearness — there must be no am- 
biguity, no opportunity for a wrong interpretation. From 
this viewpoint the four types fulfill every requirement. 
Their meaning cannot be misunderstood. To any one 
with normal intelligence their significance may be made 
perfectly clear. Any argument when once put in terms of 
the four types may be spelled out with mathematical pre- 
cision. In consequence it is of prime importance that 
the four types not only be well understood, but that a 
certain facility be gained in reducing ordinary conversa- 
tion to some one of these types. 

( 1 ) Indefinite and Elliptical Propositions. 

It is known that every logical proposition must be ex- 
pressed in terms of the four elements — quantity sign, 
logical subject, copula and logical predicate, consequently 
the four types A, E, I and O which epitomize every form 
of logical proposition, are expressed in terms of these 
four elements. But in common conversation often the 
quantity sign, as well as the copula, is omitted. See 
section 3. 

Propositions without the quantity sign are called indefi- 
nite, while those with the suppressed copula may be 
termed elliptical propositions. Both may be made logical 
as the attending illustrations will indicate : 



130 



Logical Propositions 



Illogical 

Indefinite 

Men are fighting animals. 

Lilies are not roses. 

Good is the object of moral 
approbation. 

Perfect happiness is impos- 
sible. 

Elliptical 

Fashion rules the world. 

Trees grow. 

Children play. 

Some men cheat. 



Logical 

All men are fighting ani- 
mals. (A) 

No lilies are roses. (E) 

All good is the object of 
moral approbation. (A) 

In all cases perfect happi- 
ness is impossible. (A) 

All fashions are ruling the 

world. (A) 
All trees are plants zuhich 

grow. (A) 
All children are playful. 

, (A) 

Some men are persons who 
cheat. (I) 



Here it is noted that the logical form of some proposi- 
tions is not always the most forceful. Often the logical 
form gives an awkward construction and should be re- 
sorted to only for purposes of logical argument. 

The reduction of either kind to the logical form must 
be determined by the meaning of the proposition. As a 
usual thing the indefinite is universal (either an A or an 
E) in meaning, while the problem of the elliptical is to 
give it in terms of the copula, expressed with as little 
awkwardness as possible. 

General truths, because attended with no quantity sign, 
might be classed as indefinite propositions, though theii 



Propositions Which do not Conform 131 

universality is so apparent that they may be unhesitatingly 
classed as universals. 

Illustrations : 

"Things equal to the same thing are equal to each 
other." 

"Trees grow in direct opposition to gravity." 

"Honesty is the best policy." 

"A stitch in time saves nine." 

Because the indefinite proposition is so frequently of a 
general nature, it is sometimes classed as general rather 
than indefinite. 

Sir William Hamilton would class the indefinite as an 
indesignate proposition. 

(2) Grammatical Sentences. 

The grammarian divides sentences into five kinds; 
namely, declarative, interrogative, imperative, optative, 
exclamatory. But logic recognizes only the declarative, as 
it has already been seen that the four logical types are 
declarative in nature. A logical proposition, then, is al- 
ways a sentence, but all sentences are not logical proposi- 
tions. The four kinds of sentences which are not logical 
propositions may be usually reduced to one of the four 
types as the attending illustrations will indicate : 

Illogical Logical 

Interrogative. Do men have the The question is asked, Do men 

power of rea- have the power of reason?* 

son? (A) 

Imperative. "Thou shalt not All men are commanded not to 

steal." steal, or you are one who 
should not steal. (E) 



Men do have the power of reason. 



132 Logical Propositions 

Optative. "I would I had a I am one who desires a million 

million." dollars. (A) 

Exclamatory. "Oh, how you You are one who frightened 

frightened me!" me. (A) 

(3) Individual Propositions. 

An individual proposition is one which has a singular 
subject; e. g., Abraham Lincoln was an honest man. 
Peter the Great was Russia's greatest ruler. The maple 
tree in my yard is dying of old age. These propositions, 
having a singular term as subject, are individual or singu- 
lar in nature. As the predicate refers to the whole of the 
logical subject, individual propositions are classed as 
universal. 

(4) Plurative Propositions. 

Plurative propositions are those introduced by "most," 
"few," "a few," or equivalent quantity signs. For exam- 
ple, "Most birds are useful to man" ; "Few men know how 
to live" ; "A few of the prisoners escaped," are plurative 
propositions. "Most" means more than half, while "few" 
and "a few" mean less than half. In either case the prop- 
osition is particular. Stated logically, the illustrative 
propositions would take the form of "Some birds are use- 
ful to man"; "Some men do not know how to live"; 
"Some of the prisoners escaped." 

The reader will observe the difference in significance 
between few and a few. The former is negative in char- 
acter and when introducing a proposition makes it a par- 
ticular negative (O). The latter always introduces a 
particular affirmative (I). 



Propositions Which do not Conform 133 

(5) Partitive Propositions. 

Partitive propositions are particulars which imply a 
complementary opposite. These arise through the am- 
biguous use of ail-not, some and few. Ail-not may some- 
times be interpreted as not all and sometimes as no. To 
illustrate: The proposition, "All men are not mortal," is 
distinctly a universal negative or an E, while the propo- 
sition, "All that glitters is not gold," is a particular nega- 
tive or an O. The logical form of the first is, "No men 
are mortal," and of the second, "Some glittering things 
are not gold." When used in the "not-all" sense, the prop- 
osition is partitive because if the O-meaning is intended 
the I is implied. For example, "All that glitters is not 
gold," is partitive because the statement implies that some 
glittering things are gold (I) as well as the complement, 
"Some glittering things are not gold" (O). A knowledge 
of both the affirmative and negative aspects is taken for 
granted in the statement of either the one or the other. 

"Ail-not," then, is negative in any case, but universal 
when it means no and particular when it means not all. 
Any proposition is partitive in nature when the quantity 
sign is not all, or ail-not interpreted as the equivalent of 
not all. 

It may be observed here that all has two distinct 
uses. First, it may be used in a collective sense; 
second, in a distributive sense. For example: All is used 
in the collective sense in such propositions as, "All the 
members of the football team weighed exactly one ton," 
or "All the angles of the triangle are equal to two right 
angles." Using all in the distributive sense would make 



134 Logical Propositions 

true these : "All the members of the football team weigh 
more than 140 pounds" ; "All the angles of a triangle are 
less than two right angles." All is used collectively when 
reference is made to an aggregate, but distributively when 
reference is made to each. 

The quantity sign some is likewise ambiguous, as it may 
mean (1) some only — some, but not all, or (2) some at 
least — some, it may be all or not all. When "some" is 
used as the quantity sign of any particular proposition 
which has been accepted as logical, the second meaning, 
"some at least," is always implied. This interpretation of 
"some" will be explained more in detail in a succeeding 
section. 

When some is used in the sense of some only, the parti- 
tive nature of the proposition is apparent, as both I and O 
are implied. For example, with reference to the human 
family, to say that "some only are wise" necessitates an 
investigation, which leads to the discovery that some are 
wise, while others are not wise. If the proposition be 
an I, then its complementary O is implied, or if it be an 
O, the I is implied. 

Few given as a sign of a plurative proposition also 
serves as a sign of the partitive. The plurative aspect is 
prominent when it is said that "Few men can be million- 
aires" and emphasis is placed upon the meaning that "Most 
men cannot be millionaires." But when emphasis is given 
to "few," as meaning few only rather than the most are 
not, then the I and the O are both implied; e. g., Some 
men become millionaires, but the most do not. 

To put it in a word, "ail-not," "some" and "few" intro- 



Propositions Which do not Conform 135 

duce partitive propositions when the meaning implies both 
an I and an O. When treating such in logic the meaning 
whiclr seems to be given the greater prominence must be 
accepted. Surely in the statement, "All that glitters is 
not gold," the O-interpretation is the one intended; 
namely, "Some things which glitter are not gold." 
Illustrations : 

(1) "All men are not honest." 

(2) "Few men live to be a hundred." 

(3) "Some men are consistent." 

The first proposition with the emphasis placed upon 
all suggesting that some men are not honest, is the in- 
tended proposition while some men are honest is the im- 
plied. In reducing it to the logical form the intended 
proposition is the one which should be used. 

With the emphasis upon few and some, the second and 
third propositions may be interpreted as follows: (2) 
Intended proposition, Some men do not live to be a 
hundred. Implied proposition, Some men do live to be 
a hundred. (3) Intended proposition, Some men are 
consistent. Implied proposition, Some men are not con- 
sistent. 

(6) Exceptive Propositions. 

These are introduced by such signs as all except, all but, 
all save. To wit: (1) "All except James and John may 
be excused"; (2) "All but a few of the culprits have 
been arrested"; (3) "All birds save the English sparrow 
are serviceable to man" are exceptive propositions. 

Exceptive propositions are universal when the excep- 
tions are mentioned. Universal propositions necessitate a 



136 Logical Propositions 

subject more or less definite, as the predicate of such must 
refer to the whole of a definite subject. It follows that 
in exceptive statements definiteness is secured when the 
exceptions are mentioned, therefore it becomes clear how 
all such propositions must be universal. Of the illustra- 
tions, the first and third propositions are universal. Any 
exceptive proposition is particular when the exceptions 
are referred to in general terms or when the subject 
is followed by et cetera. The second illustrative proposi- 
tion is particular. 

(7) Exclusive Propositions. 

Of all propositions which vary from the logical form 
the exclusive is the most misleading. Exclusives are ac- 
companied by such words as "only," "alone," "none but," 
and "except." Their peculiarity rests in the fact that ref- 
erence is made to the whole of the predicate, but only to a 
part of the subject. For example, in the exclusive propo- 
sition, "Only elements are metals," metals is referred to 
as a whole while elements is considered only in part. The 
true meaning is "Some elements are all metals," or to put 
it in logical form, "All metals are elements." The easiest 
way to deal with an exclusive is to interchange subject 
and predicate {convert simply) and call the proposition 
an A. 
Process Illustrated : 

Exclusive Proposition Reduced to Logical Form 

1. None but high school gradu- All who enter Training School 

ates may enter Training must be high school grad- 

School. uates. 

2. Only first-class passengers All parlor cars are for first- 

are allowed in parlor cars. class passengers. 



Propositions Which do not Conform 137 

3. Residents alone are licensed All who are licensed to teach 

to teach. are residents. 

4. No admittance except on All who have business may be 

business. admitted. 

5. Only bad men are not-wise. All who are not-wise are bad 

men. 

6. Only some men are wise. All who are wise are men. 

It is claimed by good authority that the real nature of 
the exclusive is best expressed by negating the subject and 
calling the proposition an E; e. g., exclusive: "Only ele- 
ments are metals"; logical form: "No not-elements are 
metals" (E). In a succeeding chapter it is explained 
how an E admits of first simple conversion and then 
obversion. The following illustrate these two processes: 

Original E: "No not-elements are metals." 
Simple conversion: "No metals are not-elements." 
Obversion: "All metals are elements." 

From this it may be seen that the statement, "The 
easiest way to deal with an exclusive is to interchange 
subject and predicate and call the proposition an A," is 
substantially correct. 

(8) Inverted Propositions. 

The poet often employs the inverted proposition, illus- 
trated by the following: "Blessed are the merciful;" 
"Great is this man of war." An interchanging of subject 
and predicate makes these poetical constructions logical; 
e. g., "All the merciful are blessed;" "This man of war 
is great." 

Note. — The student should not be misled by the rela- 
tive clause. Often it may be interpreted as a part of the 



Logical Propositions 



i£> ex. 



predicate rather than the subject. To wit: "No man 
friend who betrays a confidence"; clearly the logical 
subject is no man who betrays a confidence. 

7. PROPOSITIONS WHICH ARE NOT NECESSARILY 
ILLOGICAL. 

(i) Analytic and Synthetic Propositions. 

An analytic proposition is one in which the predicate 
gives information already implied in the subject. Thus, 
"Fire burns" "Water is zvet" "A triangle has three 
angles" are analytic propositions because the predicates 
do not give added information to one who has any con- 
ception of the subjects. Because the attribute mentioned 
by the predicate is an essential one, analytic propositions 
are sometimes termed essential propositions . Other 
names for the same kind of proposition are verbal and 
explicative. 

A synthetic proposition is one in which the predicate 
gives information not necessarily implied in the subject. 
"Fire protects men from the wild animal." "A cubic 
foot of water weighs 62^/2 lbs." "The sum of the interior 
angles of a triangle is equal to two right angles." These 
are synthetic because a common conception of the mean- 
ing of the subject would not need to include the informa- 
tion given by the predicate. Other names for synthetic 
propositions are accidental, real and ampliative. 

The distinction between analytic and synthetic propo- 
sitions is not so clear as would on first thought appear. 
"Fire burns" might give added information to the child 
or savage who knows only of the light emitted by fire* 



Proportions Which are not Necessarily Illogical 139 

To them, then, the proposition would be synthetic. The 
distinction must be based upon the assumption that the 
same words mean about the same thing to people in 
general. 

This analytic-synthetic division of propositions finds a 
significance in the domain of philosophy. To the logician 
the distinction is of slight importance save in the so- 
called verbal disputes, viz. : disputes which turn on the 
meaning of words. 

(2) Modal and Pure Propositions. 

A modal proposition states the mode or manner in 
which the predicate belongs to the subject. The signs of 
modal propositions are the adverbs of time, place, degree, 
manner. Illustrations: "James is walking rapidly." 
"Honesty is always the best policy." "Aristotle was 
probably the greatest thinker of ancient times. " 

A pure proposition simply states that the predicate 
belongs, or does not belong, to the subject. Illustrations : 
"James is walking." "Honesty is the best policy." 
"Aristotle was the greatest thinker of ancient times." 

Some logicians refer to modal propositions as being 
such as indicate degrees of belief. Such words as "prob- 
ably," "certainly," etc., would indicate their modality. 

As logic has to do with the pure proposition and not 
the modal, the difference of opinion is of little import. 

(3) Truistic Propositions. 

A truistic proposition is one in which the predicate re- 
peats the words and the meaning of the subject. Illus- 
trations: "A man is a man," "A beast is a beast," "A 
traitor is a traitor," "What I have done I have done." 



140 Logical Propositions 

The truistic proposition is of little importance except 
in cases where the subject is used extensionally while the 
predicate is used intensionally. In the illustration, "A 
man is a man," the subject merely stands for a member 
of the man family, while the predicate may indicate cer- 
tain manly qualities. Against such ambiguities the 
logician must be on guard. 

8. THE RELATION BETWEEN SUBJECT AND PREDI- 
CATE. 

In Chapter 5 the extension and intension of terms was 
explained. The student recalls, for instance, that the 
term "man" may be used to denote objects, as "white 
man," "black man," "red man," etc. In this sense the 
term "man" is used extensionally. But when made to 
stand for the attributes "rationality," "power of speech," 
etc., the term "man" is used intensionally. 

In, considering the relation between subject and predi- 
cate it is customary to employ the terms in an extensional 
sense only, since such a restriction serves the purpose of 
syllogistic reasoning and conversion. 

Let us, then, give attention to the extension of the 
subject and predicate of the categorical propositions 
A, E, I, O. 

( 1 ) The Universal Affirmative or A Proposition. 

All S is P symbolizes the A proposition. This may be 
interpreted as meaning that all of the subject belongs to a 
part of the predicate, or that all of the subject belongs to 
all of the predicate. The first interpretation is the usual 
one and may be illustrated by the following propositions : 



The Relation Between Subject and Predicate 141 

1. "All men are mortal." 

2. "All trees grow/' 

3. "All metals are elements." 

It is obvious that the subjects of these propositions in- 
clude every specimen of the particular class mentioned. 
For example: The subject all men includes every speci- 
men of the human family; all trees includes every object 
of that class ; all metals covers everything which the scien- 
tist classes as such. In the three propositions, then, refer- 
ence is made to the whole subject but to only a part of 
the predicate, as other beings beside men, such as the 
horse, are mortal ; and other plants aside from trees, such 
as the sun flower, grow ; other substances, namely oxygen, 
are elements. 

For the sake of making the logical meaning of the four 
propositions clearer, recourse may be made to Euler's 
diagrams, so named because the Swiss mathematician and 
logician, Leonhard Euler, first used them. 

The first illustration of the A proposition, "All men are 
mortal," may be represented by two circles, a larger circle 
standing for the predicate, mortal, and a smaller circle 
entirely inside the larger representing the subject, men. 
Thus: 




Fig. 1. 



142 Logical Propositions 

It is evident that all of the smaller circle belongs to the 
larger. This diagram will then fit any proposition where 
it may be said that all of the subject belongs to a part of 
the predicate, or which may be symbolized as "All S is 
some P." (All the subject is some of the predicate.) 

The student knows that circles are plane surfaces and 
when such a statement as "All men are mortal" is given, 
reference is made to only that part of the "mortal" circle 
which is directly underneath the "men" circle. Nothing 
has been said relative to the remaining part of the 
"mortal" circle. 

"A" propositions which may be interpreted as meaning 
"All S is all P" are called co-extensive A's because the 
subject and predicate are exactly equal in extension. Such 
propositions are best illustrated by definitions ; e. g. : 
i. "A man is a rational biped." 

2. "A trigon is a polygon of three sides." 

3. "Teaching is the art of occasioning those activities 
which result in knowledge, power and skill." 

To represent the meaning of the co-extensive A by the 
Euler diagram, two circles of the same size may be drawn, 
one coinciding at every point with the other. If the first 
circle is drawn heavily in black and the second dotted in 
red, it will make clear to the eye that there are two circles. 

(2) The Universal Negative or E Proposition. 

"No S is P" best symbolizes the E proposition, though 
sometimes the universal negative is written "All S is not 
P." This latter form, as has been explained, is ambigu- 
ous and therefore illogical. 

"No S is P" surely means that no part of the subject 



The Relation Between Subject and Predicate 143 

belongs to any part of the predicate and no part of the 
predicate belongs to any part of the subject. The subject 
and predicate are mutually exclusive. 

The following illustrate the E proposition : 

1. "No man is immortal." 

2. "No true teacher works for money." 

3. "No thorough student can remain unwise." 

The E proposition may be represented by two circles, the 
one entirely without the other as in Fig. 2 : 

( Man ] 

Fig. 2. 

(3) The Particular Affirmative or I Proposition. 

This may be symbolized as ce Some S is P," and consid- 
ered as meaning that a part of the subject belongs to a 
part of the predicate. It has already been noted that 
"some" is ambiguous and that its logical signification is 
"some at least." (It may be all or it may not be all.) 
For example, the only logical interpretation which can be 
placed on "Some men are wise" is, that the investigation 
has resulted in finding only a part of the man family 
wise. Whether or not all are wise is unknown as the 
entire field has not received attention. In no case can it 
be assumed that all the others are not wise. 



144 Logical Propositions 

The I proposition illustrated: 
i. "Some men are wise." 

2. "Some animals are vertebrates." 

3. "Some teachers are inspiring." 

The meaning of the I proposition may be represented by 
two circles intersecting each other : 




Fig. 3. 

The significant feature of the diagram is the shaded 
part which represents a part of the "men" circle as be- 
longing to a part of the "wise" circle. The unshaded part 
of each circle is the unknown field. 

(4) The Particular Negative or O Proposition. 

The common symbolization of the O is "Some S is not 
P." Put in statement form: Some of the subject is ex- 
cluded from the whole of the predicate. Here, as in the 
I, the same logical import must be given to some; e. g., 
in the proposition, "Some men are not wise," our knowl- 
edge is comfined to the group who are not wise. Whether 
or not the others are wise or not-wise is unknown. 

Illustrations of the O proposition : 

1. "Some men are not wise." 

2. "Some laws are not just." 

3. "Some novels are not helpful." 



The Relation Between Subject and Predicate 145 

The significance of the O proposition may be shown by 
two intersecting circles as in Fig. 4 : 




Fig. 4. 

A similar diagram represents the I proposition, the only 
difference being in the part shaded. In the O proposition 
the investigated field is all of the "men" circle outside of 
the "wise" circle, while in the I proposition the known 
field is that part of the "men" circle inside the "wise" 
circle. 

In comparing the four diagrams the student will note 
that the affirmative propositions are inclusive, while the 
negative propositions are exclusive. 

(5) The Distribution of Subject and Predicate. 

A term is said to be distributed when it is referred to 
as a definite whole. 

In the proposition, "All men are mortal," the subject 
all men is considered as a whole. "All men" stands for 
every specimen of the human race; not a single one has 
been left out. Again, the whole is definite ; any one, 
if he were given the time and opportunity, could ascertain 
by actual count just how many "all men" represented. 

It should be observed that if the word definite is not 
incorporated in the definition of a distributed term, there 



146 Logical Propositions 

is afforded an opportunity for error. The attending illus- 
trations will make this clear : 

1. "All the students except John and James are dis- 

missed." 

2. "All the students except John, James, etc., are 

dismissed." 

The subject of the first proposition is distributed, while 
the subject of the second is undistributed. Reasons: The 
first subject, "All the students except John and James," is 
referred to as a whole and that whole is definite, there- 
fore, it is distributed; the second subject, "All the stu- 
dents except John, James, etc.," is referred to as a whole, 
but as the whole is not definite, the term is not distri- 
buted. Because all is the quantity sign of the second sub- 
ject the casual observer might easily be misled in desig- 
nating it as a distributed term. 

Here it may be well to explain that when reference is 
made to subject or predicate the logical subject or predi- 
cate is meant. Unless this is constantly kept in mind 
error results; e. g., in the proposition, "All white men are 
Caucasians," the logical subject is "white men," not 
"men." If the subject were "men," it would be undis- 
tributed, as the whole of the man family is not considered, 
but the actual subject, being "white men," is distributed 
because the predicate refers to all white men. 

Recurring to the illustration, "All men are mortal," we 
have concluded that the subject "all men" is distributed. 
The predicate, "mortal," however, is undistributed, as 
reference is made to it only in part; i. e., there are other 
beings aside from men that are mortal, such as "trees," 



The Relation Between Subject and Predicate 147 

"horses," "dogs," etc. In all A propositions of the type 
of u all men are mortal" the subject is distributed while 
the predicate is undistributed. This relation is clearly 
shown by the diagrammatical illustration, Fig. I. Here 
all of the "men" circle is identical with only a part of the 
"mortal" circle. In other words, the whole of the "men" 
circle is considered, while reference is made to only a part 
of the "mortal" circle. 

In the case of the co-extensive A both subject and 
predicate are distributed. Relative to the co-extensive 
"All men are rational animals," it could likewise be said 
that "all rational animals are men," or that "all men are 
all of the rational animals." Reference is thus made to 
all of the definite predicate as well as to all of the definite 
subject. 

In the E propositions, such as "No men are immortal," 
the whole of the subject is excluded from the whole of 
the predicate. This makes evident the fact that both 
terms are distributed. See Fig. 2. 

The I proposition, such as "Some men are wise," con- 
cerns itself with only a part of the subject and only a 
part of the predicate, consequently neither subject nor 
predicate is distributed. This relation is verified by the 
representation, Fig. 3. 

In the O proposition the subject is undistributed, while 
the predicate is distributed. For example, in the propo- 
sition, "Some men are not wise," "some men" would 
indicate that only a part of the logical subject is under 
consideration. But the predicate is distributed because 
"some men" is denied of the whole of the predicate, 



148 



Logical Propositions 



"wise." This may become clear by studying Fig. 4. Here 
all of the shaded part which stands for the subject, "some 
men," is excluded from the whole of the "wise" circle. 
But all of the shaded part is only a part of the entire "men" 
circle, consequently the subject which the shaded part 
represents (some men) is undistributed. The predicate, 
"wise," however, is distributed, as the subject is excluded 
from every part of it. It is well to remember that not, 
when used with the copula, distributes the predicate which 
follows it. 

If the student is to succeed in testing the value of argu- 
ments, he must ever have "at the tip of his tongue" his 
knowledge of the distribution of the terms of the four 
logical propositions. With this in view the following 
schemes are offered: 

I. 





Subject 




Predicate 


A 


distributed 




undistributed 


E 


distributed 




distributed 


I 


undistributed 




undistributed 


O 


undistributed 




distributed 


A 


distributed 


II. 


undistributed 


O 


undistributed 




distributed 


E 


distributed 




distributed 


I 


undistributed 




undistributed 


A 


All S is P 


III. 




E 

I 


No S is P 

1 — 1 1 — 1 

Some S is P 




| 


O 


Some S is not P 





The Relation Between Subject and Predicate 149 

Referring to scheme II it may be observed that A and 

O contradict each other; i. e., where A is distributed O 

is undistributed and vice versa. A similar relation exists 

between E and I. 

In scheme III the bracket ^__ under the symbol indicates 
the term which is distributed. 

IV. As a fourth scheme a "key word" might be adopted. 
Any of these three might be used: (1) saepeo, or (2) 
asebinop, or (3) uaesneop. The significance of "saepeo" 
is this : "s" stands for subject distributed, "p" for predi- 
cate distributed, "a," "e" "0" for the logical propositions 
where any distribution occurs. Putting the letters together 
gives this: subject distributed of propositions A and E, 
predicate distributed of propositions E and O. 

Similarly, "asebinop" stands for this : "as," a distributes 
its subject; "eb," e distributes froth; "in" i distributes 
neither; "op" distributes the predicate. 

In the coined word "uaesneop" appear six letters which 
compose "saepeo," and the letters have the same signifi- 
cance. The two additional letters, u and n, stand for uni- 
versal and negative. The interpretation of the entire 
word, therefore, is this: "uaes" the wniversals a and e 
distribute their subjects; neop, the negatives e and dis- 
tribute their predicates. 

It seems to me that the last word is the most helpful as 
it emphasizes the two facts which are the most used; 
namely, (1) Only the universals distribute their subjects; 
(2) Only the negatives distribute their predicates. 

If the student will visualize "uaesneop" so thoroughly 
as never to forget it, he will not experience difficulty in 



150 Logical Propositions 

determining the distribution of the terms of the four 
logical propositions. 

9. OUTLINE. 

Logical Propositions. 

(1) The nature of logical propositions. 

(2) Kinds of logical propositions. 

Categorical 

Hypothetical 

Disjunctive 

(3) The four elements of a categorical proposition. 

(4) Logical and grammatical subject and predicate distin- 
guished. 

(5) The four kinds of categorical propositions. 

Universal affirmative A 

Universal negative E 

Particular affirmative I 

Particular negative O 

(6) Propositions which do not conform to the logical type. 

Indefinite and elliptical. 

Grammatical sentences 

Individual 

Plurative 

Partitive 

Exceptive 

Exclusive 

Inverted 

(7) Propositions not necessarily illogical. 

Analytic and synthetic. 
Modal and pure. 
Truistic 
(8)) The relation between subject and predicate of the four 
logical propositions. 

Euler's diagrams. 

Distribution of subject and predicate. 

Uaesneop 

Asebinop 

Saepeo 



Summary 151 



10. SUMMARY. 



(1) A logical proposition is a judgment expressed in words. 

(2) The three kinds of logical propositions are categorical, 
hypothetical, disjunctive. 

A categorical proposition is one in which the assertion is 

made unconditionally. 
A hypothetical proposition is one in which the assertion 

depends upon a condition. 
A disjunctive proposition is one which asserts an alterna- 
tive. 
The most common word-signs of the categorical proposition 
are "all," "no," "some" and "some-not," of the hypothetical, "if" 
and of the disjunctive, "either — or." 

(3) Every logical categorical proposition has the four ele- 
ments: quantity sign, subject, copula and predicate. 

The quantity sign indicates the extension of the proposition; 
the logical subject is that of which something is affirmed or 
denied; the logical predicate is the term which is affirmed or 
denied of the subject; the copula is always some form of "to be" 
and is used to connect subject and predicate. "Not" is some- 
times used with the copula. 

The statements of ordinary conversation are usually not ex- 
pressed in terms of the four elements, but must be, before they 
can be used in testing arguments. 

(4) One word usually constitutes the grammatical subject 
while a word with all its modifiers goes to make up the logical 
subject. The verb with any predicate word is the grammatical 
predicate. The logical predicate is all which follows the copula — 
it may include the predicate-word and all its modifiers as well 
as the modified object. 

(5) Categorical propositions are divided into four kinds; uni- 
versal affirmative (A), universal negative (E), particular affirma- 
tive (I), particular negative (O). For the sake of brevity these 
four are respectively denoted by the vowels A, E, I, O. 

An A proposition is one in which the predicate affirms 

something of all of the logical subject. 
An E proposition is one in which the predicate denies 

something of all of the logical subject. 



152 Logical Propositions 

An I proposition is one in which the predicate affirms 

something of a part of the logical subject. 
An O proposition is one in which the predicate denies 
something of a part of the logical subject. 
Every proposition must be reduced to one of the four types 
before it can be used as a basis of argumentation. 

It is incumbent on the student to recognize these four types 
with precision and accuracy. 

(6) There are a few proposition types which are recognized 
as being illogical in form. These may be denned as follows : 

(1) An indefinite proposition is one without the quantity 

sign. It usually may be classed as universal. 

(2) An elliptical proposition is one in which the copula 

is suppressed. 

(3) An individual proposition is one which has a singular 

subject. It is universal in content. 

(4) Plurative propositions are those introduced by "most," 

"a few," or some equivalent quantity sign. These 
are particular in meaning. 

(5) Partitive propositions are particulars which imply a 

complementary opposite. These arise through the 
ambiguous use of "ail-not," "some" and "few." 
"Ail-not" sometimes means "no," while at other times it may 
mean "not-all." If the quantity sign means the latter, then it 
introduces a partitive proposition. 

"Some" may mean "some only" or "some at least" The latter 
is the logical meaning. The former interpretation makes the 
proposition partitive. When "few" means "few only," it is 
partitive in nature. 

(6) Exceptive propositions are those introduced by such 

signs as "all except," "all but," "all save," etc. They 
are universal only when the exceptions are 
mentioned. 

(7) Exclusive propositions are those introduced by such 

words as "only," "alone," "none but" and "except." 
In an exclusive the predicate and not the subject is 
distributed. Consequently the easiest way to make 
an exclusive logical is to interchange subject and 
predicate and call it an A. 



Summary 153 

(8) An inverted proposition is one where the predicate 

precedes the subject. Interchanging them gives the 

logical form. 

Of the grammatical sentences only the declarative is logical. 

The relative clause, though out of place, must be used with the 

word it modifies. 

(7) There are other propositions, though not illogical, to 
which the logician usually gives some attention. These may be 
defined as f ollows : 

(1) An analytical proposition is one in which the predi- 

cate gives information already implied in the sub- 
ject. 

(2) A synthetic proposition is one in which the predicate 

gives information not implied in the subject. 

(3) A modal proposition is one which states the manner 

in which the predicate belongs to the subject. The 
adverbs of time, place, degree and manner are the 
signs of the modal proposition. 

(4) A pure proposition simply states that the predicate 

belongs or does not belong to the subject. 

(5) A truistic or tautologous proposition is one in which 

the predicate repeats the words and meaning of the 
subject. 

(8) In considering the relation which may exist between sub- 
ject and predicate, the two terms are employed in extension only, 
as this use best serves the interests of inference. 

The extensional relation between subject and predicate of the 
four logical propositions may be stated as follows : 

Ordinary A — All of the subject belongs to a part of the 
predicate. 

Co-extensive A — All of the subject belongs to all of the 
predicate. 

E — None of the subject belongs to any part of the predi- 
cate. 

I — Some of the subject belongs to some of the predicate. 

O — Some of the subject is excluded from the whole of 
the predicate. 



154 Logical Propositions 

In general it may be said that the affirmative propositions are 
inclusive while the negatives are prelusive. 

A term is said to be distributed when it is referred to as a 
definite whole. 

"A" distributes the logical subject only, "E" both logical sub- 
ject and logical predicate, "I" neither logical subject nor logical 
predicate, "O" the logical predicate only. The co-extensive "A" 
distributes both subject and predicate. 

It is essential that the student know by heart the distribution 
of the terms of the logical propositions. Some keyword like 
uaesneop may be used as an aid to the memory. This means 
the wniversals A and E distribute their subjects, while the nega- 
tives E and O distribute their predicates. 

11. ILLUSTRATIVE EXERCISES. 

(la) Examine the following list of propositions with a view to 
classifying them as "A's," "E's," "I's" or "O's." 
E 1. "None of the inmates voted." 
A 2. "Benj. Franklin was the best educated American." 
/ 3. "Some doctors deem it right to lie to their patients." 
A 4. "All earnest teachers need to observe the teaching 

of others." 
/ 5. "Some politicians are honest." 
A 6. "Fools rush in where angels fear to tread." 
O 7. "Some proverbs are not true to life." 
E 8. "No man should infringe upon the rights of others." 
I recall that an affirmative proposition in which the predicate 
refers to the whole of the subject is an A, while one where the 
predicate refers to only a part of the subject is an I. Further, 
a negative proposition where the predicate refers to the whole of 
the subject is an E, while one in which the predicate refers to 
only a part of the subject is an O. With these facts in mind, I 
classify the propositions as indicated. 

(lb) In a similar manner classify as to quantity and quality 
the following: 

(1) "All worthy workers grow to look like their work." 



Illustrative Exercises 155 

(2) "Every dog has his day." 

(3) "Some of the presidents were not popular." 

(4) "No unskilled laborer can afford to own an auto- 

mobile." 
(5) "Some of the 'election prophets' were sadly mis- 
taken." 
(2a) Classify the following propositions and make the illogical, 
logical : 

(1) "Only first-class passengers may ride in parlor cars." 

(2) "Haste makes waste." 

(3) "Few men know how to act under stress." 

(4) "All which seems to ring true is not true." 

(5) "Members alone are admitted." 

(6) "None but men of integrity need apply." 

(7) "Horses trot." 

(8) "Blessed are they which are persecuted for righteous- 

ness sake." 

The first proposition is an exclusive and may be made logical 
by converting and calling it an A, viz. : "All who ride in parlor 
cars are first-class passengers." (A) 

The second is indefinite and elliptical and is made logical by 
prefixing the universal quantity sign and expressing in terms of 
the four elements. The logical form is, "All who make haste 
are those who are wasteful." (A) 

The third is plurative in nature and means, "Most men do not 
know how to act under stress." It would be classed as an O. 

The fourth is partitive in nature because of the ambiguous use 
of "all — not." It means, "Some who seem to ring true are not 
true." (O) 

The fifth is an exclusive. By converting and changing to an 
A the proposition takes the logical form, "All who are admitted 
are members." 

The sixth is likewise an exclusive, the logical form being,' "All 
who apply must be men of integrity." 

The seventh is an elliptical proposition. Logical form : "All 
horses are trotting animals." 

The eighth is an inverted or poetical proposition. It is made 
logical by interchanging subject and predicate. Logical form: 
"Those who are persecuted for righteousness sake are blessed." 



156 Logical Propositions 

(2b) Classify the attending propositions and change to the 
logical form, if necessary: 

(1) "Only truthful men are honest." 

(2) "The stokers alone were saved." 

(3) "All who run do not think." 

(4) "Honesty is the best policy." 

(5) "They laugh that win." 

(6) "The good alone are happy." 

(7) "Knowledge is power." 

(8) "Only the actions of the just smell sweet and blossom 

in the dust." 

12. REVIEW QUESTIONS. 

(1) Define and illustrate logical propositions. 

(2) Define and exemplify the three kinds of logical prop- 
ositions. 

(3) What are the usual quantity signs of the four kinds 
of propositions? 

(4) Name and define the four elements of a logical proposi- 
tion. 

(5) Select from the printed page five propositions which 
are not expressed in terms of the four elements, and so express 
them. 

(6) Distinguish between logical and grammatical subject; 
likewise between logical and grammatical predicate. 

(7) Define and illustrate the four kinds of categorical prop- 
ositions. 

(8) What makes an understanding of the four logical prop- 
ositions so important? 

(9) Give the unusual quantity signs of the logical propositions. 

(10) What should guide one in making an indefinite proposi- 
tion logical? 

(11) How are general truths usually classified? 

(12) Change birds fly to the logical form. 

(13) How many and what kinds of grammatical sentences are 
logical? 

(14) How would the logician deal with interrogative sen- 
tences ? 



Review Questions 157 

(15) Give illustrations of individual propositions. How are 
they usually classified? 

(16) Explain the logical mode of dealing with the plurative 
proposition. 

(17) Exemplify the ambiguity of "ail-not," "some" and "few." 

(18) Why are propositions introduced by "ail-not," "some" 
and "few" called partitive? 

(19) Use "all" in both a partitive and collective sense. Which 
signification has logic adopted? 

(20) When are exceptive propositions universal and when par- 
ticular ? 

(21) What is an exclusive proposition? 

(22) Explain by circles the exclusive. 

(23) Tell in full how to change an exclusive to logical form. 

(24) Tell how the logician would deal with such poetical ex- 
pressions as "Blessed are the pure in heart," "Tell me not in 
mournful numbers," "Strenuous is the man of state." 

(25) What distinction does the logician make between analytic 
and synthetic propositions? 

(26) Illustrate the difference between the so-called modal and 
pure propositions. 

(27) Explain and illustrate the truistic proposition. 

(28) Show by circles the relation existing between the subject 
and predicate of all the logical propositions. 

(29) State in good English the relation between the subject 
and predicate of all the logical propositions. 

(30) Relative to the distribution of terms apply the words 
"uaesneop" and "asebinop." Which one is the more serviceable? 

(31) Distinguish between the grammatical and logical subject. 

(32) Explain by circles the distribution of the terms of the 
four logical propositions. 

(33) The statement, "A part of the subject is excluded from 
the whole of the predicate," describes which proposition? Ex- 
plain how it indicates that the predicate is distributed. 

13. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Show that a judgment may be an individual notion as 
well as a general notion. 



158 Logical Propositions 

(2) Many logicians classify logical propositions in this wise: 

("Categorical 
Propositions , T _ , . , 

{Conditional f Hypothetical 
*■ (Disjunctive 

Give arguments for and against such a classification. 

(3) "All men are bipeds" is a judgment of extension, while 
"Man is wise" is a judgment of intension. Explain. 

(4) "To be logical is to be pedantic." Discuss this. 

(5) Why is the proposition, "He runs," illogical? Make it 
logical. 

(6) Point out the reasons for calling, "White men are Cau- 
casians," a particular proposition. 

(7) What makes it necessary to change the propositions of 
ordinary conversation to those of the four logical types? 

(8) Some would call the individual proposition particular. 
Argue the question. 

(9) Make a list of five propositions in common speech and 
show how their partitive implication may mislead. 

(10) Explain by circles some only and some at least. 

(11) Explain how "et cetera" may change a universal to a 
particular proposition. . 

(12) "The real nature of an exclusive is best shown by ne- 
gating the subject and calling the proposition an E." Give argu- 
ments for and against this statement. 

(13) Show that with the immature mind all propositions must 
be synthetical. 

(14) Explain how a proposition may be truistic in form but 
not in meaning. 

(15) Show by the Euler diagram how easy it is for the care- 
less student to think that an "O" does not distribute its predicate. 

(16) Explain by the use of two pads (a small yellow one and 
a large white one) the distribution of terms. 

(17) When the logician makes reference to the subject of a 
proposition, show that he should exercise care in designating it 
as the logical subject. 



CHAPTER 9. 

IMMEDIATE INFERENCE OPPOSITION. 

1. THE NATURE OF INFERENCE. 

Inference is the thought process of deriving a judgment 
from one or two antecedent judgments. 

The process is simply a matter of expressing explicitly 
in a final judgment, a truth that was implied in one or two 
previous judgments. To exemplify: From the ante- 
cedent truth, that "All teachers should be fair minded," 
one may derive a consequent truth that "This teacher, 
Albert White, should be fair minded." Or from the state- 
ment, "All men are mortal," one may derive the judg- 
ment, "No men are immortal." Because the ground is 
wet we conclude that it has rained. If all dogs are quad- 
rupeds then surely some dogs are quadrupeds. Finally 
from the two propositions, "All training school students 
are high school graduates," and "Mary Jones is a train- 
ing school student," we are led to conclude that "Mary 
Jones is a high school graduate." 

2. IMMEDIATE AND MEDIATE INFERENCE. 

It has been noted that a truth may be derived from d 
consideration of one or two antecedent judgments. To 
illustrate further: From the judgment, "All men are 
fallible," we may derive the conclusion that "No men are 
infallible"; or, from the two judgments, "All men are 
fallible," and "Socrates was a man," we may readily infer 

159 



i6o 



Immediate Inference 



that "Socrates was fallible." These two modes of infer- 
ence take the names of immediate inference and mediate 
inference. Let us express these two kinds in equation 
form: 

I. 
Ordinary Form. Equation Form, Using 

Initial Letters. 
Antecedent judgment: All men 

are fallible. 
Conclusion: No men are infalli- 
ble. 

II. 
First antecedent judgment: All 

men are fallible. 
Second antecedent judgment : 
Socrates was a man. 
Conclusion : Socrates was falli- 
ble. 
Giving attention to the antecedent judgments of the 
second argument it is noted that the terms "f and "S" 
are referred to the common term "m" In logic this 
common term is known as the middle term. As there is 
but one antecedent judgment in the first argument there 
can be no common or middle term. The first argument 
is an illustration of immediate inference; the second of 
mediate inference. This suggests the definitions: 

Immediate inference is inference without the use of a 
middle term. 

Mediate inference is inference by means of a middle 
term. 



All m are f 
No m are i 



All m are f 
S was m 

.'. S was f 



The Forms of Immediate Inference 161 

3. THE FORMS OF IMMEDIATE INFERENCE. 

Many logicians recognize four forms of immediate in- 
ference. These four forms are (i) opposition, (2) ob- 
version, (3) conversion, (4) controversion* 

(1) IMMEDIATE INFERENCE BY OPPOSI- 
TION. 
We have learned that to be logical all categorical asser- 
tions must be reduced to some one of the four proposi- 
tions, A, E, I, O. If these four logical propositions be 
given the same subject and predicate, certain definite rela- 
tions will become evident; therefore, Opposition is said 
to exist between propositions which are given the same 
subject and predicate, but differ in quality, or in quantity, 
or in both. 
The following illustrative outline will make this clear: 
1. 2. 

Original Proposition. Opposite in Quantity. 

I. All men are mortal. (A) Some men are mortal. (I) 
II. No men are immortal. (E) Some men are not immortal. (O) 

III. Some men are wise. (1) All men are wise. (A) 

IV. Some men are mortal. (I) All men are mortal. (A) 

V. Some men are not wise. (O) No men are wise. (E) 

VI. Some men are not immor- No men are immortal. (E) 

tal. (O) 

3. 4. 

Opposite in Quality. Opposite in Both. 

No men are mortal. (E) Some men are not mortal. (O) 

All men are immortal. (A) Some men are immortal. (I) 

Some men are not wise. (O) No men are wise. (E) 

Some men are not mortal. (O) No men are mortal. (E) 

Some men are wise. (I) All men are wise. (A) 

Some men are immortal. (I) All men are immortal. (A) 



* Sometimes called contraposition. 



1 62 Immediate Inference 

Granting the truth of the propositions in the first col- 
umn, it follows that those in the second column differ in 
quantity. That is, in "Some men are mortal," a smaller 
number of men is referred to than in "All men are mor- 
tal." A similar variation in quantity obtains with the 
other propositions in the second column. Moreover, the 
propositions in the third column are the negative of the 
corresponding ones in the first; while the fourth column 
propositions differ from the first in both quantity and 
quality. Thus opposition exists to a greater or less de- 
gree between all. We may now ask ourselves the question, 
"When the propositions are related to each other in oppo- 
sition which ones are true and which ones are false ?" Giv- 
ing attention to the propositions in row "I," we note that if 
the universal affirmative, "All men are mortal," is true, 
then the particular affirmative, "Some men are mortal," is 
likewise true; because of the principle, "What is true of 
the whole of the class is true of a part of that class." 
But the universal negative, "No men are mortal," and the 
particular negative, "Some men are not mortal," are both 
false. Briefly stated: If A is true, then I is true, but, 
both E and O are false. 

Regarding row "II" we may conclude that if E is true, 
then O is likewise true, but both A and I are false. 

As to rows "III" and "IV," granting the truth of the I 
propositions, "Some men are wise" and "Some men are 
mortal," we are able to assert that of the two A proposi- 
tions, "All men are wise," and "All men are mortal," the 
first is false while the second is true. A is, therefore, in- 
determinate, or doubtful. Of the O propositions, "Some 



The Forms of Immediate Inference 



163 



men are not wise," is true while, "Some men are not mor- 
tal," is false. Therefore, O is doubtful. Both of the E 
propositions are false. Hence, the conclusion relative to 
rows "III" and "IV" is : If I is true, A and O are doubt- 
ful, while E is false. 

Concerning rows "V" and "VI" it will be seen without 
further explanation that if O is true, then E and I are 
doubtful and A is false. 

The Scheme of Opposition. 

The conditions of opposition are easily comprehended 
and remembered when recourse is made to the following 
scheme : 

A E I O 

If A be true 
If E be true 
If I be true 
If O be true 

To use the above scheme, read horizontally from left 
to right. For example : If A be true, then all in the row 
opposite obtains; that is, A is true, E is false, I is true, 
and O is false. (We take it for granted that the student 
will see that the first column belongs to A, the second to 
E, the third to I, and the fourth to O.) If E be true, 
then A is false, E is true, I is false, O is true, etc. 

The whole of opposition is comprehended in two facts 
which are based upon one principle. This is the principle : 
Whatever may be said of the entire class may be said of 



true 


false 


true 


Jafee"" 


false 


Ixtie 


fafee" 


true 


doubt 


fajse^ 


true 


doubt 


false^ 


doubt 


doubt 


^true 



164 



Immediate Inference 



a part of that class. To put it in another way : Whatever 
is affirmed of all may be affirmed of some, or, Whatever 
is denied of all may be denied of some. To illustrate: 
Accepted truth: All planets rotate. (A) 
Accepted inference: Some planets rotate. (I) 

or 
Accepted truth: No planet is a sun. (E) 
Accepted inference : Some planets are not suns. (O) 
These are the two facts : First, a particular affirmative 
may be derived from a universal affirmative. Second, 
a particular negative may be derived from a universal 
negative. Or, more briefly: An I may be derived from 
an A, and an O from an E. 
Square of Opposition. 

Aristotle represented the relations of the four logical 
propositions by what is termed the square of opposition. 

A Contraries E 




The Forms of Immediate Inference 165 

Viewed from the standpoint of the square, the relations 
may be summed up as follows : 

1. Contrary Propositions. 

Why so named. 

As related to each other, A and E are said to be con- 
trary because they seem to express contrariety to the 
greatest degree. 

Relation stated. 

If one is true, the other must be false, but both may be 
false. 

Illustrations. 

(1) If one is true, the other must be false; e. g., if A 
is true, as "All metals are elements," then E is false, as 
"No metals are elements." Or, if E is true, as "No birds 
are quadrupeds," then A is false, as "All birds are 
quadrupeds." 

(2) Both may be false. If A is false, as "All men are 
wise/' then E may be false, as "No men are wise." 

2. Subcontrary Propositions. 

Why so named. 

Propositions I and O are said to be related to each 
other in a subcontrary manner because they are contrary 
as to each other and "under" their universals A and E. 

Relation stated. 

If one is false, the other must be true, or, both may 
be true. 

Illustrations. 

(1) If one is false, the other must be true. 

If I is false, as "Some metals are compounds," then, O 
is true, as "Some metals (at least) are not compounds." 



1 66 Immediate Inference 

Or, if O is false, as "Some metals are not elements," 
then I is true, as "Some metals are elements." 

(2) Both may be true. 

If I is true, as "Some men are wise," then O also may 
be true, as "Some men are not wise." 

3. Subalterns. 

Why so named. 

Etymologically considered subaltern means under the 
one, thus proposition I is under A, and O is under E. 

Relation stated. 

First Relation. 

Subalterns are related to each other as are the uni- 
versal and particulars ; hence, 

(1) If the universal is true, the particular under it is 
also true ; while if the particular is true, the corresponding 
universal may, or, may not, be true. 

Illustrations. 

(a) If the universal is true, the particular under it is 
true. 

If A is true, as "All metals are elements," then I is 
true, as "Some metals are elements." Or, if E is true, as 
"No metals are compounds," then, O is also true, as 
"Some metals (at least) are not compounds." 

(b) If the particular is true, the corresponding uni- 
versal may, or, may not, be true. 

If I is true, as "Some men are wise," or, "Some men 
are mortal," then A may be false, as "All men are wise," 
or, A may be true, as "All men are mortal." Or, if O is 
true, as "Some men are not wise," or, "Some men are not 



The Forms of Immediate Inference 167 

immortal," then E may be false, as "No men are wise" ; 
or, true, as "No men are immortal." 

Second Relation. 

(2) If the universal is false, the particular under it 
may or may not be true, but, if the particular is false, 
the universal above it must be false. 

Illustrations. 

(a) If the universal is false, the particular under it 
may or may not be true. 

If A is false, as "All metals are compounds," or "All 
men are wise," then I may be false, as "Some metals are 
compounds," or, I may be true, as "Some men are wise." 
Or, if E is false, as "No men are mortal," or, "No men 
are wise," then O may be false, as "Some men are not 
mortal," or, O may be true, as "Some men are not wise." 

(b) If the particular is false, the universal above it 
must be false. 

If I is false, as "Some men are trees," then A is 
false, as "All men are trees." Or, if O is false, as "Some 
men are not bipeds," then E is also false, as "No men are 
bipeds." 

4. Contradictory Propositions. 

Why so named. 

The propositions A and O, likewise E and I, are called 
contradictory propositions because they oppose each other 
in both quantity and quality. They are mutually opposed 
to each other or absolutely contradictory. 

Relation stated. 

If one is true the other must be false. 



1 68 Immediate Inference 

Illustrations. 

(i) A and O compared. 

If A is true, as "All metals are elements," then, O is 
false, as "Some metals are not elements." Or, if O is 
true, as "Some metals are not compounds," then A is 
false, as "All metals are compounds." 

(2) E and I compared. 

If E is true, as "No birds are quadrupeds," then I is 
false, as "Some birds are quadrupeds." Or, if I is true, 
as "Some birds are bipeds," then E is false, as "No birds 
are bipeds." 

The chief value of the square of opposition springs 
from the contradictory propositions. The square shows 
conclusively that any universal affirmative assertion (an 
A) may best be contradicted by proving a particular nega- 
tive (an O). For example: To satisfactorily refute the 
statement that, in this section, all birds migrate to the 
south in winter, it would be sufficient to prove that the 
English sparrow and starling do not migrate to the south. 
The square likewise makes evident that any universal 
negative (an E) may be conclusively denied by establish- 
ing the truth of a particular affirmative (an I). To illus- 
trate : The easiest way to prove the falsity of "No trusts 
are honest" is to present facts showing that at least trusts 
A and B are honest. 

The Individual Proposition. 

An individual proposition is one with an individual sub- 
ject such as "Aristotle was wise." In logic, the indi- 
vidual proposition is classed as a universal. This seems 
to be a bit irregular, as with the individual proposition 



The Forms of Immediate Inference 169 

there is no particular, while, the strictly logical universal 
always implies a particular. Because of this variation 
from the true logical form the relations, as indicated by 
the square of opposition, do not apply to the individual 
proposition. For example: According to the square A 
and E are contrary, but, when individual, A and E con- 
tradict each other, as "Aristotle was wise" (A) — "Aris- 
totle was not wise" (E). 



CHAPTER 10. 

IMMEDIATE INFERENCE (CONTINUED) OBVERSION, CON- 
VERSION, CONTRAVERSION AND INVERSION. 

(2) IMMEDIATE INFERENCE BY OBVER- 
SION. 

Obversion is the process of changmg a proposition from 
the affirmative form to its equivalent negative or from 
the negative form to its equivalent affirmative. 

Some authorities refer to this process as "Inference by 
Privitive Conception/' but Obversion seems to be a better 
term. 

Obversion is based upon the principle that two nega- 
tives are equivalent to one affirmative. With this double 
negative principle in mind let us experiment with the four 
logical propositions, A, E, I, O. 

The A Proposition. 

Example: "All thoughtful men are wise." Insert the 
double negative and the proposition reads: "All thought- 
ful men are not not-wise." Changed to the logical form 
this becomes: "No thoughtful men are not-wise." Sim- 
plified and we have, finally : "No thoughtful men are un- 
wise." Thus by the process of obversion we have passed 
from the original proposition, "All thoughtful men are 
wise," to "No thoughtful men are unwise." In the first 
proposition the subject "thoughtful men" is denied of the 
predicate "unwise." Assuming that "unwise" is the con- 
tradictory of "wise," then : "What is affirmed of a predi- 

170 



Immediate Inference by Obversion 171 

cate may be denied of its contradictory." Recourse to cir- 
cles will make this clearer. In the previous chapter it has 
been suggested that not bisects the world. For example : 
What can not be included in the wise class may be placed 
under the not-wise or unzvise class. Likewise a circle 
bisects space — there is the space inside the circle and the 
space outside the circle. Let the space inside the circle 
represent all wise beings, then the space outside the circle 
would represent all not-wise or unwise beings ; e. g., 

unwise 
( Wise J 



unwise wise unwise 



unwise 
Fig. 5. 



Now representing thoughtful men by a smaller circle 
and placing it inside the larger we have, 



unwise 



unwise #*«i««y#«*/— unwise 




172 Immediate Inference 

Referring to Fig. 6 we note that all of the smaller cir- 
cle belongs to the larger or that none of the smaller circle 
belongs to the space outside of the larger. Hence the two 
propositions: "All thoughtful men are wise" (A), and 
"No thoughtful men are unwise" (E) have virtually the 
same meaning though the same subject is related to 
different predicates. 

The use of the positive or negative form depends upon 
circumstances. Often the negative puts the thought in a 
more forceful way. 

In passing from, "All thoughtful men are wise," to 
"No thoughtful men are unwise," it was necessary to pre- 
fix not to the predicate wise and substitute for not its 
equivalent tin. If the original predicate were unwise or 
not-wise, then the reverse order of dropping the un or 
not could be followed. This process of prefixing the not 
to an affirmative predicate or of dropping the not from a 
negative predicate is referred to as negating the predi- 
cate. Before substituting in, im, un, etc., for not, one 
must make sure that the substitution really gives the con- 
tradictory; there are some logicians who claim that un- 
wise, for instance, is not the contradictory of wise. 

In comparing the first proposition with the second it 
is observed that the first is an A, while the second is an 
E, also that the predicate of the first was negated to form 
the predicate of the second. Thus the rule: Negate the 
predicate and change A to E. 

To sum up: 

The obversion of an A proposition. 



Immediate Inference by Obversion 173 

1. Principle: 

Two negatives are equivalent to one affirmative. 

2. Rule: 

Negate the predicate and change the A to an E by 
using the sign no instead of all. 

3. Process illustrated. 

The Original Proposition (A) The Obverse (E) 

All men are mortal. No men are immortal. 

All maples are trees. No maples are not-trees. 

All teachers should be sympa- No teacher should be un- 

thetic. sympathetic. 

All pain is unpleasant. No pain is pleasant. 

All men are imperfect. No men are perfect. 

All birds are feathered ani* No birds are non- 

mals. feathered animals. 

All men are not-trees. No men are trees. 

All scalene triangles are non- No scalene triangles are 

equilateral. equilateral. 

The E Proposition. 

It is obvious that the process of obverting an E is sim- 
ply the reverse of obverting an A. Consequently, the 
same principle obtains ; whereas the process may be illus- 
trated by reading the foregoing illustrations reversely. 

The rule for obverting E is : Negate the predicate and 
change the E to an A by changing the sign no to all. 

The I Proposition. 

Let us note the result when the double negative prin- 
ciple is applied to the I proposition. 

Original : "Some men are wise." 

Adding two negatives: "Some men are not not-wise." 



174 Immediate Inference 

The foregoing simplified: "Some men are not unwise." 
In comparing the first proposition with the last it is ob- 
served that the first is an I while the last is an O; it is 
also observed that the predicate of the first was negated 
in order to form the predicate of the last. Thus the rule : 
"Negate the predicate and change the I to an O." 
The use of circles may make this clearer: 

unwise 



unwise Mori Hi Ia/j.*;* I unwise 




The significant part of Fig. 7 is that which is inked. 
Here we have represented the part of the "men" circle 
which is common to the "wise" circle. Thus the inked 
part represents "Some men are wise." If the inked part 
is entirely inside of the "wise" circle, no part of it can 
belong to the "unwise" space without. Thus the obverse, 
"Some men are not unwise." 

Summary. 

The obversion of an I proposition. 

1. Principle: 

Same as with A. 

2. Rule: 

Negate the predicate and change the I to an O. 



Immediate Inference by Obversion 175 

3. Process illustrated. 
The Original Proposition (I) The Obverse (0) 

Some water is pure. Some water is not impure. 

Some curves are perfect. Some curves are not imper- 
fect. 
Some friends are loyal. Some friends are not dis- 

loyal. 
Some men are true. Some men are not not-true. 

Some precious stones are Some precious stones are 

imperfect. not perfect. 

Some plants are not-trees. Some plants are not trees. 
Some boys are not-honest. Some boys are not honest. 
It must be borne in mind that when "nof ' is used without 
the hyphen it makes the proposition negative, because 
when "unhyphened" "not" must be thought of in connec- 
tion with the copula and not in connection with the predi- 
cate ; while "nof attached to the predicate with a hyphen 
simply makes the predicate negative without affecting 
the quality of the proposition ; e. g., "Some plants are not 
trees" is a negative proposition, while "Some plants are 
not-trees ,, is an affirmative proposition with a negative 
predicate. 

It may not be clearly seen how it is possible, by follow- 
ing the rule given, to pass from such a proposition as 
"Some plants are not-trees," to "Some plants are not 
trees/' Let us illustrate the steps : 

1. The original: "Some plants are not-trees." 

2. Negating predicate : "Some plants are trees." 

3. Changing to an O : "Some plants are not trees." 



176 Immediate Inference 

Dropping the not from "1" and then adding it again to 
"2" is simply putting into operation the double negative 
idea, so that there is no violation of the principle. 

The Proposition. 

O bears the same relation to I that E bears to A. The 
principle involved is the same. The process is illustrated 
by reading reversely the scheme of illustrations under I. 
The rule is as follows : To obvert an O negate the predi- 
cate and cliange the O to an I by eliminating the not. 

Summary of Obverting the Four Logical Propositions. 

1. Principle: 

Two negatives are equivalent to one affirmative. 

2. Rules: 



f (1) A to E 
J ( 2 



Negate the predicate J (2) E to A 
and change 1 (3) I to O 
^ (4) O to I 

(3) IMMEDIATE INFERENCE BY CONVER- 
SION. 

Conversion is the process of inferring from a given 
proposition another which has, as its subject, the predicate 
of the given proposition, and, as its predicate, the subject 
of the given proposition. It is simply a matter of trans- 
posing subject and predicate. The original proposition is 
called the convertend while the derived proposition is 
named the converse. 

The process of conversion is limited by two rules. 
First rule. No term must be distributed in the converse 
which is not distributed in the convertend. Second rule. 
The quality of the converse must be the same as that of 



Immediate Inference by Conversion 177 

the convertend. More briefly: (1) Do not distribute an 
undistributed term. (2) Do not change the quality. 

We recall that a term is distributed when it is referred 
to as a definite whole. An undistributed term is referred 
to only in part. The principle underlying rule "1" there- 
fore, is the one which forms the basis of inference by 
opposition ; namely, "Whatever may be said of the entire 
class may be said of a part of that class." The converse 
of this is not true, that is, "What is said of part of a class 
cannot be said of the whole of that class.'' When we dis- 
tribute an undistributed term we are saying of the whole 
class what was said only of a part of that class. This is 
fallacious. On the other hand, we may say of a part 
what was said of the whole, or "undistribute" a distributed 
term. , 

We recall that the conclusion of the whole matter of 
inference by opposition was, that only an I could be in- 
ferred from an A and only an O from an E, or to put it 
in another way: Only an affirmative from an affirmative 
and only a negative from a negative. This establishes 
the truth of the second rule in conversion: "Do not 
change the quality." 

Let us apply the two rules to the four logical proposi- 
tions. 

Converting an A proposition. 

Take as a type, "All horses are quadrupeds." Here the 
subject " horses" is distributed, but the predicate "quad- 
rupeds" is undistributed. In transposing subject and 
predicate we cannot distribute the term "quadrupeds," 
according to the rule which says, "Do not distribute an 



178 Immediate Inference 

undistributed term." Hence in interchanging subject and 
predicate we cannot say, "All quadrupeds are horses," 
but must limit the assertion to, "Some quadrupeds are 
horses." Logicians call this process Conversion by Limita- 
tion. 

Conversion by Limitation Exemplified Further. 
Convertend Converse. 

All metals are elements. Some elements are metals. 

All bees buzz. Some buzzing insects are 

bees. 
All men are fallible. Some fallible beings are 

men. 
All good teachers are sym- Some sympathetic persons 

pathetic. are good teachers. 

The conclusions from the foregoing are these: First, 
the usual mode of converting an A is to interchange sub- 
ject and predicate, limiting the latter by the word "some" 
or a word of similar significance. Second, this mode is 
called conversion by limitation. Third, the converse of an 
A is an I. 

The Co-extensive A. 

In the conversion of A propositions there is the one ex- 
ception of "co-extensive A's," such as truisms and defini- 
tions. It will be remembered that with these both subject 
and predicate are distributed; hence, they may be inter- 
changed without limiting the predicate by "some." To 
illustrate: The converse of the truism, "A man is a man," 
is "A man is a man," while the converse of the definition, 
"A man is a rational animal," is "A rational animal is a 
man." This mode of interchanging subject and predicate 



Immediate Inference by Conversion 179 

without limiting the latter is called Simple Conversion. 
The ordinary A proposition is thus converted by limita- 
tion, while the co-extensive A is converted simply. 
Converting an E proposition. 

As both terms of the E proposition are distributed it 
is not possible to violate the rule of distribution. It is to 
be remembered that no fallacy is committed by "undis- 
tributing" a term which is already distributed. 
Illustrations. 

Convertend. Converse. 

No men are immortal. No immortals are men. 

Simply. 
No birds are quadrupeds. No quadrupeds are birds. 

Simply. 
No metals are compounds. No compounds are metals. 

Simply. 
No men are immortal. S#me immortals (at least) 

are not men. Limitation. 
No birds are quadrupeds. Same quadrupeds are not 

birds. Limitation. 
No metals are compounds. Some compounds are not 

metals. Limitation. 
Three facts are evident relative to the converting of an 
E. First: An E proposition may be converted either 
simply or by limitation. Second: E may be converted 
into either E or O. Third: If the converse is an O then 
is the inference a weakened one, being particular when it 
could just as well be universal. 
Converting an I proposition. 
With an I proposition neither term is distributed. 



180 Immediate Inference 

Thus care must be used lest an undistributed term in the 
convertend be distributed in the converse. Illustrations: 

Convertend. Converse. 

Some men are wise. Some wise beings are men. 

Some teachers scold. Some who scold are teachers. 

Some high school graduates Some who enter college are 

enter college. high school graduates. 

Some Americans live simply. Some who live simply are 

Americans. 

From the foregoing we conclude first, that I is con- 
verted simply; second, that I is converted into I. 

The Proposition. 

With an O proposition the subject is undistributed while 
the predicate is distributed. This condition presents a 
peculiar difficulty. Consider, for example, the O proposi- 
tion, "Some men are not wise." Convert this into, "Some 
wise beings are not men," and the undistributed subject of 
the convertend, which is "men," becomes the distributed 
predicate of the converse. Thus the proposition cannot 
be converted without violating the rule for distribution. 

A Summary of How the Four Logical Propositions 
May be Converted. 

i. A. The ordinary A proposition may be con- 
verted by limitation only. The co- 
extensive A may be converted simply. 

2. E. The E proposition is converted simply. 

The E may also be converted by limita- 
tion, but the inference thus obtained is 
weakened. 

3. /. The I proposition may be converted simply 

only. 

4. O. The O proposition cannot be converted. 



Immediate Inference by Contr aversion 181 

(4) INFERENCE BY CONTRAVERSION. 
(Contraposition). 

This mode of inference is usually referred to as in- 
ference by contraposition, but contraversion, indicating 
more definitely the nature of the process, is a better term. 
Contraversion involves two steps: First, obversion; sec- 
ond, conversion. The same principles and rules evident 
in these two processes obtain in inference by contraver- 
sion. The following scheme, therefore, ought to be 
sufficient to make the matter clear: 

Inference by Contraversion. 

1. The Given Proposition. 2. Obverted. 

A. All men are mortal. No men are immortal. 

All trees are plants. No trees are not-plants. 

E. No men are infallible. All men are fallible. 

No men are trees. All men are not-trees. 

I. Some men are wise. Some men are not not-wise. 

O. Some water is not pure. Some water is impure. 

Some houses are not white. Some houses are not-white. 

3. Converted; giving the contraverse of the original 
proposition. 
No immortals are men. 
No not-plants are trees. 
Some fallible beings are men. 
Some not-trees are men. 
An O cannot be converted, consequently 

the contraversion of an I is impossible. 
Some impure liquids are water. 
Some not-white buildings are houses. 
It is indicated in the foregoing scheme that "I" cannot 
be contraverted. This is due to the fact that the obverse 



182 



Immediate Inference 



of an I is an O, and it will be remembered that "O" 
cannot be converted. All the other propositions admit of 
contraversion. 

4. EPITOME OF THE FOUR PROCESSES OF IMMEDIATE 
INFERENCE IN CONNECTION WITH THE FOUR 
LOGICAL PROPOSITIONS. 



Proposition 
symbolized 



Name of 
Process 



Inference 
symbolized 



Principle 
involved 



A All S is P* 



Opposition 
Obversion 



Some S is P (i) 
No S is not-P (E) 



Conversion by Some P is S (i) 

Limitation 

Contraversion No not-P is S (E) 



What is said of all may be 
said of some. 

Two negatives are equivalent 
to one affirmative. 

An undistributed term cannot 
be distributed. 

Same principles which obtain 
in obvertingf A and convert- 
in? E. 



E 


No Sis P 


Opposition 


Some S is not P (0) 


What is said of all may be 
said of some. 






Obversion 


All S is not-P (A) 


Two negatives are equivalent 
to one affirmative. 






Simple Conversion 


No P is S (E) 


Distribution not affected. 






Contraversion 


Some not-P is S (l) 


An undistributed term cannot 
be distributed. 


I 


Some S is P 


Opposition 


Doubtful 


None. 






Obversion 


Some S is not not-P (o) 


Two negatives are equivalent 
to one affirmative. 






Conversion 


Some P is S (i) 


Distribution not affected. 






Contraversion 


Impossible 


None. 


O 


Some S is not P 


Opposition 


Doubtful 


None. 






Obversion 


Some S is not-P (i) 


Two negatives are equivalent 
to one affirmative. 






Conversion 


Impossible 


None. 






Contraversion 


Some not-P is S (i) 


Same as in obversion of O 
and conversion of I. 



*S" represents any subject and "P" any predicate. 



Inference by Inversion 183 

Inference By Inversion. 

Some logicians treat of a form of immediate inference known 
as inversion though it is of small importance and of little 
practical value. 

The process can be applied only to propositions A and E. In 
the one case the contradictory subject is limited by "some" and 
then denied of the predicate, whereas, in the other case, the 
contradictory subject is merely affirmed of the predicate. 
Illustrations. 

The Given Proposition. The Inverse. 

I. All S is P. (A) Some not-S is not P. (O) 

All planets rotate. Some not-planets do not rotate. 

II. No S is P. (E) Some not-S is P. (I) 

No men are immortal. Some not-men are immortal. 

From the foregoing we are able to conclude that the inverse 
of "A" is found by negating the subject and changing to an "O" ; 
while the inverse of "E" is found by negating the subject and 
changing to an "I." 

5. OUTLINE. 

Immediate Inference — Opposition — Obversion, Conversion, 
contraversion and inversion. 

1. The Nature of Inference. 

2. Immediate and Mediate Inference. 

3. The Forms of Immediate Inference. 

(1) Opposition. 

(a) Scheme of Opposition. 

(b) Square of Opposition. 

(2) Obversion. 

(3) Conversion. 

(a) Simply. 

(b) By Limitation. 

(4) Contraversion. 
Inversion. 

6. SUMMARY. 

1. Inference is the thought process of deriving a judgment 
from one or two antecedent judgments. 



184 Immediate Inference 

2. Immediate inference is inference without the use of a 
middle term. Mediate inference is inference by means of a 
middle term. 

3. The four common forms of immediate inference are (1) 
opposition, (2) obversion, (3) conversion, (4) contraversion. 

(1) The name opposition stands for certain definite relations 
which exist between the logical propositions v/hen they are given 
the same subject and predicate. The one principle underlying 
opposition is : Whatever is said of the entire class may be said 
of a part of that class. The two statements which sum up oppo- 
sition are first, an I may be derived from an A; and second, an 
O may be derived from an E. 

The crucial fact made obvious by the square of opposition is 
that A and O are mutually contradictory; likewise E and I. 

(2) Obversion is the process of passing from an affirmative to 
its equivalent negative or from a negative to its equivalent 
affirmative. "Two negatives are equivalent to one affirmative," 
is the basic principle of obversion. 

The proposition A may be obverted by negating the predicate 
and changing to an E. "E" is obverted by negating the predicate 
and changing to an A. "I" is obverted by negating the predicate 
and changing to an O. "O" is obverted by negating the predicate 
and changing to an I. 

(3) Conversion is the process of inferring from a given propo- 
sition another which has as its subject the predicate of the 
given proposition and as its predicate the subject of the given 
proposition. 

Conversion is limited by the two rules, (1) do not distribute 
an undistributed term; (2) do not change the quality. 

To convert an A interchange subject and predicate, limiting 
the latter by some, or a word of like significance. This is called 
conversion by limitation. 

The co-extensive A may be converted without limiting the 
predicate. This is called simple conversion. 

An E proposition may be converted either simply or by limita- 
tion. When converted by limitation the inference is a weakened 
one. 

An I proposition is converted simply only. 



Summary 185 

The O proposition does not admit of conversion. 

(4) Immediate inference by contraversion is a process involv- 
ing first obversion and then conversion. 

"A," "E" and "O" may be controverted ; "I" cannot be con- 
travened. 

7. ILLUSTRATIVE EXERCISES. 

(la) From the antecedent judgment, "All weeds are plants," I 
am able to derive by immediate inference these judgments: (1) 
"All weeds are not not-plants," or "No weeds are not plants." (2) 
"No not-plants are weeds." (3) "Some plants are weeds." (4) 
"Some weeds are plants." 

(lb) "All vertebrates have a backbone." From the foregoing 
judgment derive immediately five different conclusions. 
(2a) "All good citizens try to vote," 

^'Albert White is a good citizen/' 
Hence, "Albert White will try to vote." 
I know that the above is an example of mediate inference be- 
cause the two antecedent judgments make use of the middle 
term, "good citizen" 

(2b) Why is the following illustrative of mediate inference? 
"All wise men are close observers," 
"All wise men are thoughtful," 
Hence, "Some thoughtful men are close observers." 
(3a) Derive immediate inferences by opposition from the fol- 
lowing : 

(1) "Good men are wise." 

(2) "No teacher can afford to be unjust." 

(3) "All birds fly." 

(4) "None of the inner planets are as large as the earth." 
I first determine that "1" and "3" are A propositions, while 

"2" and "4" are E's. Then I recall that by opposition an I may 
be derived from an A and an O from an E. Hence, the 
inferences are: 

(1) "Some good men are wise." 

(2) "Some teachers cannot afford to be unjust." 

(3) "Some birds fly." 

(4) "Some of the inner planets are not so large as the 

earth." 



1 86 Immediate Inference 

'3b) Derive by opposition inferences from the following: 

(1) "No true woman will neglect her home for society." 

(2) "All patriotic men love the flag." 

(3) "Fools rush in where angels fear to tread." 
(4a) Obvert the following: 

(1) "All earnest teachers are diligent students." 

(2) "No self-respecting man can afford to be careless in 

his personal appearance." 

(3) "Some of the great teachers of the past did not 

practice what they preached." 

(4) "Some weeds are beautiful." 

I determine first the logical character of each proposition, 
finding the first to be an A, the second an E, the third an O and 
the fourth an I. Then I recall that in obversion the predicate 
must always be negated and an A must be changed to an E or 
an E to an A ; also an I must be changed to an O or an O to an I. 
Hence, the obverse of each proposition is : 

(1) "No earnest teacher is a not-diligent student." 

(2) "All self-respecting men can afford to be not-careless 
(careful) in their personal appearance." 

(3) "Some of the great teachers of the past did not- 
practice (failed to practice) what they preached." 

(4) "Some weeds are not not-beautiful." 
(4b) Infer by obversion from the following: 

(1) "All roses are beautiful." 

(2) "None of the members of the stock exchange are 

dishonest." 

(3) "Some pupils are not industrious." 

(4) "Some teachers are tactful." 
(5a) Convert the following: 

(1) "All that glitters is not gold." 

(2) "All good men are wise." 

(3) "Some books are to be chewed and digested." 

(4) "No man is perfectly happy." 

It is first necessary to determine the logical character of each 
proposition. Carelessness might lead one to call the first propo- 
sition an A because it is introduced by the quantity sign "all." 
But on second thought we note that the meaning is to the effect 
that some glittering things are not gold; this is an O. It is clear 



Illustrative Exercises 187 

that the second is an A, the third an I and the fourth an E. It 
is now expedient to recall the rules regarding conversion. These 
are, (1) do not distribute an undistributed term; (2) do not 
change the quality. We may now attempt to interchange the 
subject and predicate of each proposition, with the following 
results : 

(1) Conversion impossible. 

(2) "Some wise men are good men." 

(3) "Some things to be chewed and digested are books." 

(4) "No perfectly happy being is a man." 

When attempting to convert proposition (1), I find that the 
subject which is undistributed becomes distributed, hence the 
rule pertaining to distribution is violated. This conclusion is 
verified by recalling the fact that an O proposition cannot be con- 
verted. The second proposition, being an A, is converted by limita- 
tion; while the third and fourth are converted simply, as is the 
natural procedure with all Fs and E's. 

(5b) Convert these propositions : 

(1) "Blessed are the meek." (All the meek are blessed.) 

(2) "None but material bodies gravitate." (All gravita- 

ting bodies are material.) 

(3) "Gold is not a compound substance." 

(4) "Usually cruel men are cowards." 

Note.. — The first proposition is poetical while the second is an 
exclusive. 

(6a) Contravert the following propositions : 

(1) "All virtue is praiseworthy." 

(2) "Some teachers are not tactful." 

(3) "A man who lies is not to be trusted." 
Contraversion consists in obverting first, and then converting; 

consequently, the contraverse of the three propositions is as 
follows : 

(1) "No unpraiseworthy deed is virtue." 

(2) "Some not-tactful persons are teachers." 

(3) "Some untrustworthy men are those who lie." 
(6b) Write the contraverse of the following: 

(1) "All honest men pay their debts." 

(2) "All men are rational." 



1 88 Immediate Inference 

(3) "Nearly all the troops have left the town." 

(4) "Some teachers are not patient." 

(7a) The attending scheme indicates the logical process and 
rule involved in passing from one proposition to another: 
A. "All men are imperfect." 



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not-men are 


perfect beings. 



Illustrative Exercises 189 

(7b) Treat in a manner similar to the above the proposition, 
"All horses are quadrupeds." 

8. REVIEW QUESTIONS. 

(1) What is inference? 

(2) What is the meaning of antecedent? 

(3) Define (1) judging, (2) a judgment. 

(4) All roses are beautiful, 

This flower is a rose, 
This flower is beautiful. 
Write this example of mediate inference in equation form. 
Name the middle term. 

(5) Define immediate inference. Illustrate. 

(6) Define mediate inference. Illustrate. 

(7) Name the five forms of immediate inference. 

(8) What principle is involved in inference by opposition? 

(9) Draw the scheme of opposition. 

(10) Make use of this scheme in deriving inferences from the 
following propositions : 

(a) "Good men are wise." 

(b) "No king is infallible." 

(c) "Cattle are ruminants." 

(d) "All who cheat the railroads are not honest." 

(11) What are contradictory propositions? Illustrate. 

(12) What would be the simplest way of disproving the state- 
ment that "No great religious teacher has been consistent?" 

(13) Why are A and E said to be contrary propositions? 

(14) Define obversion. 

(15) By what other name is obversion known? 

(16) State the basic principle of obversion. 

(17) Illustrate the process known as negating the predicate. 

(18) State the rule for obverting an A proposition. 

(19) Obvert the following: 

(1) "All the boys in my room are industrious." 

(2) "Honesty is the best policy." 

(3) "Only the industrious are truly successful." 



190 Immediate Inference 

(20) First state the rule and then obvert the following: 

(1) "Some plants are biennial." 

(2) "Planets are not suns." 

(3) "Blessed are the merciful." 

(4) "These samples are not perfect." 

(21) Define conversion. 

(22) State and illustrate the rules which condition the process 
of conversion. 

(23) Convert, if possible, the following: 

(1) "Some men practice sophistry." 

(2) "Few men know how to live." 

(3) "Some of the inhabitants are not civilized." 

(4) "All the world is a stage." 

(5) "None of my pupils failed." 

(6) "Experience is a hard taskmaster." 

(24) Wiry may co-extensive propositions be converted simply? 

(25) Describe the process of inference by contraversion. 

9. PROBLEMS FOR ORIGINAL THOUGHT AND INVESTI- 
GATION. 

(1) What ground is there for the belief that immediate in- 
ference, so called, is merely a matter of the interpretation of 
propositions ? 

(2) Is there any difference between reasoning and inference? 

(3) When the conclusion is reached that two rooms are of 
the same width, because each is five yards wide, what is the 
middle term? 

(4) Put in equation form: 

All teachers instruct, 
John Jones is a teacher, 
John Jones instructs. 
Show that the equations are not absolutely true. 

(5) Indicate the true relation between the subjects and predi- 
cates of the foregoing by using the algebraic signs > and < 

(6) Why cannot an A be derived from an I? 

(7) Why cannot an O be derived from an A? 

(8) The basic principle of obversion is "Two negatives are 
equivalent to one affirmative." Show by means of circles that 



Problems for Original Thought and Investigation 191 

this is not absolutely true ; take as an illustrative proposition, "No 
men are not mortal." 

(9) Show that agreeable and disagreeable are not contra- 
dictory terms. 

(10) Why should the logician class individual propositions as 
universal ? 

(11) Show by circles that there is a difference in signification 
between, "Some men are not wise" and Some men are not-wise." 

(12) Show by circles that the O proposition cannot be con- 
verted. 

(13) "The I proposition cannot be contraverted." Make this 
clear. 

(14) Is there any difference in meaning between, "All illogical 
work is unscholarly" and "No illogical work is scholarly?" 
Explain by circles. 

(15) State the logical process involved in passing from each 
proposition to its succeeding one: 

(1) "All men are imperfect." 

(2) "No men are perfect." 

(3) "No perfect beings are men." 

(4) "Some not-men are perfect beings." 

(5) "Some perfect beings are not-men." ' 

(6) "Some perfect beings are not men." 

(16) It is sometimes said that in sub-contraries there is really 
no opposition. Do you agree? Give arguments. 



CHAPTER 11. 

MEDIATE INFERENCE. THE SYLLOGISM. 

1. INFERENCE AND REASONING. 

Inference has been denned as both a product and a 
process. When used to indicate a process the term in- 
ference becomes synonomous with reasoning. If 
logicians could agree to confine inference to the product 
and reasoning to the process, it would remove an am- 
biguity which is more or less misleading. But since 
this has not become the custom, we shall use inference 
as indicating the process as well as the product. 

Definitions — Middle Term Explained. 

Inference is the thought process of deriving a judg- 
ment from one or two antecedent judgments. 

Mediate inference is inference by means of a middle 
term. 

Reasoning of this nature involves three terms, two 
of which are compared with a third or middle term, 
and then related to each other to form a new judgment. 
The middle term is the common unit, or the standard^ 
by which the other terms are measured. To illustrate: 
If John and James are each six feet tall, then plainly, 
they are of the same height. The standard, or middle 
term, is "six feet tall." 

2. THE SYLLOGISM. 

Just as the judgment is expressed by means of the 
proposition, so mediate inference is best expressed by 

192 



The Syllogism 193 

means of the syllogism.* The following are syllogisms: 

(1) James is six feet tall, 
John is six feet tall, 

Hence James is as tall as John. 

(2) All true teachers are just, 
You are a true teacher, 
Hence you are just. 

(3) All men are mortal, 
You are a man, 
Hence you are mortal. 

3. THE RULES OF THE SYLLOGISM. 

All syllogistic reasoning is conditioned by the follow- 
ing eight rules: 

(1) A syllogism must have three, and only three, 

different terms. 

(2) A syllogism must have three, and only three, 

propositions. 

(3) The middle term must be distributed at least 

once. 

(4) No term must be distributed in the conclu- 

sion which is not also distributed in a 
premise. 

(5) No conclusion can be drawn from two 

negative premises. 

(6) If one premise be negative, the conclusion 

must be negative; and conversely, to prove 
a negative conclusion, one of the premises 
must be negative. 



* From the Greek meaning to reason with. 



194 Mediate Inference — The Syllogism 

(7) No conclusion can be drawn from two 

particular premises. 

(8) If one premise be particular, the conclusion 

must be particular. 
These rules are exceedingly important, as their 
observance is necessary in all mediate reasoning. The 
student needs, not only to understand the meaning of 
these rules, but he needs to commit them to memory 
so thoroughly that they may be recalled without hesita- 
tion or mistake. To aid the memory, the eight rules 
may be divided into these four groups : 

I. Rules one and two relate to the composition 
of the syllogism. 
II. Rules three and four pertain to the distribution 
of terms. 

III. Rules five and six have reference to negative 

premises. 

IV. Rules seven and eight concern particular 

premises. 

4. RULES OF THE SYLLOGISM EXPLAINED. 

(1) A syllogism must have three and only three terms. 

It is common to represent the various syllogistic 
forms by symbols, the same symbols always standing 
for the same terms. In this treatment we shall let cap- 
ital G stand for the major term, as "major" means 
greater; capital S. for the minor term, as " minor " 
means smaller, and capital M for the middle term. G, 
S and M, the initial letters of greater (major), smaller 
(minor) and middle, will be the constant symbols for 



Rules of the Syllogism Explained 195 

these terms; just as A, E, I and O are used as the 
constant symbols for the four logical propositions. 

Illustration . 

Syllogism written in full: 

All men are mortal, 
Socrates is a man, 



(Therefore) Socrates is mortal. 
Syllogism symbolized: 

All M is G 
S is M 



.'. S is G 

The major term is always the predicate and the minor 
term the subject of the conclusion. The conclusion of 
the foregoing syllogism is, " Socrates is mortal." Since 
G stands for the predicate of every conclusion, then it 
stands for " mortal" the predicate of the above con- 
clusion. For a similar reason, S stands for the sub- 
ject, namely, " Socrates'' ; while M represents the middle 
term, " man." 

Since every syllogism must have three propositions, 
and since it takes two terms to form a proposition, then 
it follows that every syllogism must contain six terms. 
But, as no syllogism can have more than three different 
terms, we conclude that each term of the syllogism must 
be used twice. In the foregoing example, G thus 
appears, not only in the last proposition, or conclusion, 
but in the first proposition also. Similarly, both S and 
M occur twice. Every logical syllogism, then, contains 



196 Mediate Inference — The Syllogism 

first, a major term, which is always the predicate of the 
conclusion and appears once in the premises; second, a 
minor term, which is always the subject of the conclu- 
sion and appears once in the premises; and third, a 
middle term to which the other two terms are referred. 

There are two ways of locating the middle term; 
first, it is the term which is used in both the premises; 
second, it is the term which never appears in the con- 
clusion. Likewise, there are two ways of locating the 
major and minor terms; first, the major term is always 
the predicate and the minor term the subject of the con- 
clusion; second, the major term is usually the broader 
and the minor term the narrower of the two. If the 
major and minor terms seem to be of about the same 
extension or breadth, then the term in the first 
proposition, which is not the middle term, is the major. 

In the attending syllogisms the three terms are 
designated : 

(middle) (major) 

(1) All true teachers are sympathetic, 
(minor) (middle) 

1 1 

You are a true teacher, 
(minor) (major) 

.'. You are sympathetic. 

(major) (middle) 

(2) No shell fish are vertebrates, 

(minor) (middle) 



Rules of the Syllogism Explained 197 

All trout are vertebrates, 
(minor) (major) 

.*. No trout are shell fish. 

The necessity of having but three different terms in 
any syllogism may be understood by supposing that 
there are four different terms; then it would follow 
that there could be no standard or common link. In 
the axiom, " Things equal to the same thing are equal 
to each other," the same thing is the common standard 
or link. Two things which equal two different things 
are not equal to each other. 

The impossibility of reasoning from four terms may 
be shown by circles. 

All men are mortal. 
All trees grow. 




Fig. 8. 

These circles show that no connection can be estab- 
lished between either group. Using four terms in any 
syllogism is known as the fallacy of four terms. 

(2) A syllogism must have three and only three 
propositions. The proposition containing the major 
term is called the major premise, while the one contain- 
ing the minor term is called the minor premise. In a 
strictly logical syllogism the major premise is written 



198 Mediate Inference — The Syllogism 

first, the minor premise second and the conclusion third. 
In common parlance, however, the minor premise or 
even the conclusion may appear first. 

The conclusion of a syllogism is always preceded by 
therefore, or its equivalent, which may be written or 
understood. The premises always answer the question, 
Why is the conclusion true? The premises are often 
preceded by such words as for and because. 

The attending irregular syllogisms are arranged 
logically and the premises and conclusions indicated: 

(ia) Illogical. 

"You must take an examination because all who enter 
the school are examined and you, as I understand it, 
are planning to enter." 

(2a.) "Some of these books are not well bound, for 
they are going to pieces as no well bound book would 
do." 

(ib) Logical. 

All who enter this school are examined, Major 

premise. 
You are planning to enter this school, Minor 

premise. 
You must be examined. Conclusion. 
(2b) No well bound book goes to pieces, Major 

premise. 
Some of these books are going to pieces, Minor 

premise. 
Some of these books are not well bound. 

Conclusion. 



Rules of the Syllogism Explained 199 

The fact that all syllogisms must have three and only 
three premises follows from rule "1." One premise 
must compare the middle term with the "major"; 
another premise must compare the middle term with the 
" minor " ; while the conclusion links together the 
" major " and the " minor." 

(3) The middle term must be distributed at least 
once. The rule is usually given in this way, " The mid- 
dle term must be distributed once at least, and must not 
be ambiguous." In this treatment the last part of the 
rule has been omitted because it must be apparent to 
the student that a middle term used in two senses is 
virtually equivalent to two different terms; such an 
"ambiguous middle" would, in consequence, give a 
syllogism of four terms. 

Rules 3 and 4 are of greater importance than the 
others because they are more frequently violated. If 
the middle term is not distributed at least once, the 
fallacy is referred to as "undistributed middle" If 
the distributed major term of the conclusion is not dis- 
tributed in the major premise, then the fallacy is called, 
"illicit process of the major term" ; and finally, if the 
distributed minor term of the conclusion is not distrib- 
uted in the minor premise the fallacy is denominated an 
illicit process of the minor term." These two illicit 
processes may be abbreviated to illicit major and illicit 
minor. 

Recall that any term is distributed when it is referred 
to as a definite whole. Unless the whole of the middle 
term is considered it fails to become a common standard 



200 Mediate Inference — The Syllogism 

of comparison. This becomes clear when recourse is 
made to the circles. 
Illustration. 

Syllogism in which the middle term is not distributed: 
All men are mortal, 
All trees are mortal, 
.'. All trees are men. 
All the propositions are A's and consequently the predi- 
cates of each are undistributed, as A distributes the 
subject only. Therefore the middle term, "mortal," is 
not distributed in either of the premises and thus the 
fallacy. 
Fallacy shown by circles : 




Fig. 9. 
These circles indicate the correct meaning of the two 
premises. By them it is seen that all of the " men " 
circle belongs to the " mortal " circle and all of the 
"tree" circle belongs to the "mortal" circle, but in this case 
there is no connection between the "men" and "tree' cir- 
cles. Thus, to say that "All trees are men," is fallacious. 
We have no right to either affirm or deny the connection 
between men and trees. If "mortal" were distributed we 
would have this right as the following will make clear : 



Rules of the Syllogism Explained 201 

All men are mortal, 
No stones are mortal, 
.'. No stones are men. 

JloirtaiX f 5tones\ 




w 



Fig. 10. 

Here the middle term mortal is distributed in the 
second premise as in it the subject "stones" is excluded 
from the entire mortal territory. This conclusion is 
verified by the formal statement that " E " distributes 
both subject and predicate. Since all of the " men " 
circle belongs to the " mortal " circle and none of the 
"stones" circle belongs to the "mortal" circle then none 
of the " stones " circle can belong to the " men " circle. 

(4) No term must be distributed in the conclusion 
which is not also distributed in its premise. 

It has been affirmed that a term is distributed when 
it is referred to as a definite whole. To put it in 
another way, a term is distributed when it is employed 
in its fullest sense. It is obvious that we should not 
employ a term in its fullest sense in the conclusion when 
it has been used only in a partial sense in its premise. 
What is said of the part cannot necessarily be said of 
the whole. For example: Because some men are 
honest it does not follow that all men are honest. Of 
course the converse of this is true, namely, if it could 
be proved that all men are honest then surely it would 



202 Mediate Inference — The Syllogism 

follow that some of the men are honest. To put it 
briefly : What is true of all is true of some but what is 
true of some is not necessarily true of all. 

To distribute a term in the conclusion when it is not 
distributed in the premise where it occurs is equivalent 
to saying, " what is true of some is true of all." This 
error which violates rule " 4 " leads to the two fallacies 
of illicit process of the major and minor terms. The 
following illustrate the two fallacies. 

Syllogism illustrating illicit major: 
All trees grow, 
No men are trees, 
.'. No men grow. 
The first premise is an A and consequently its subject 
is distributed. The second premise and conclusion being 
E's have both subject and predicate distributed. Thus 
grow, as used in the conclusion, is distributed, but, as 
used in the major premise, it is not distributed. Fallacy 
shown by circles : 




Fig. 11. 
Here all of the " tree " circle belongs to the " grow " 
circle and none of the " men " circle belongs to the 
" tree " circle, hence the diagram correctly represents 



Rules of the Syllogism Explained 203 

the meaning of the two premises and shows the fallacy 
of concluding that no men grow. The "men" circle, 
being entirely within the " grow " circle, indicates that 
all men grow. Syllogism illustrating illicit minor : 
All true teachers are just, 
All true teachers are sympathetic, 
.'. All the sympathetic are just. 
Each proposition being an A distributes its subject. But 
the subject of the conclusion which is "the sympathetic" 
is not distributed in the minor premise, as an A propo- 
sition distributes its subject only. Hence the fallacy of 
illicit minor. 

Fallacy shown by circles : 




Fig. 12. 

The diagram correctly represents the two premises 
since all of the " true teacher " circle belongs to both 
the " just " and " sympathetic " circles. But all of the 
"sympathetic" circle does not belong to the "just" 
circle. Hence the fallacy. 

(5) No conclusion can be drawn from two negative 
premises. 

When two terms are both denied of a third term, it 
is quite impossible to draw any conclusion relative to 



204 Mediate Inference — The Syllogism 

the two terms, as the absolute exclusion of the third 
term eliminates any possibility of a common link or 
standard. 
The circles will make this apparent : 

No men are immortal, 

No trees are immortal, 

Wen\ 

[//nmortal] 




Fig, 13. 

" No trees are men " is the conclusion represented by 
Fig- 13. 

Other possible conclusions are, "All trees are men," 
"All men are trees" and "Some men are trees." 

It is thus seen that no definite conclusion can be 
drawn. It may now be said that when the major and 
minor terms are used in two negative premises the con- 
nection between them is indeterminate. This violation 
of rule "5" may be termed the fallacy of two negatives. 

(6) // one premise be nagtive the conclusion must 
be negative; and conversely, to prove a negative con- 
clusion one of the premises must be negative. 

Referring to the first part of this rule, it may be said 
of two terms that if one is affirmed and the other denied 
of a third term, then the two terms must be denied of 



Rules of the Syllogism Explained 205 

each other. The attending syllogism and its " circled " 
representation will throw light upon this : 
No men are immortal, 
All Americans are men, 
.'. No Americans are immortal. 




Fig. 14. 

Since none of the " men " circle belongs to the 
" immortal " circle and all of the "American " circle is 
inside the " men " circle, it is evident that none of the 
"American " circle can belong to any part of the 
" immortal " circle. Thus it is manifest that an affirma- 
tive conclusion like, "All Americans are immortal," is 
invalid. 

The converse of rule 6, " To prove a negative con- 
clusion, one of the premises must be negative," may be 
explained by the general principle in logic that when 
two terms are known to disagree, one must agree with 
a third term while the other must disagree. If both 
agreed with a third, then the conclusion would of 
necessity be affirmative. If both disagreed no conclu- 
sion could be drawn. A violation of rule 6 may be 
called the fallacy of negative conclusion. 

(7) No conclusion can be drawn from two particular 
premises. Proof : 



206 Mediate Inference — The Syllogism 

(i) All the possible combinations of the two 
particular premises I and O are, (i) IO, 
(2) OI, (3) II, (4) 00. 

"IO" considered. 

(2) Since O is a negative premise the conclusion 
would have to be negative according to rule 
6, (If one premise is negative, the conclusion 
must be negative.) 

(3) If the conclusion is negative, then its predi- 
cate, which is the major term, must be dis- 
tributed. (All negative propositions distribute 
their predicates.) 

(4) If the major term is distributed in the con- 
clusion, it must be distributed in the major 
premise, rule 4 (No term must be distributed 
in the conclusion, which is not also distributed 
in one of the premises.) 

(5) Hence two terms must be distributed in the 
premises, the major term according to (4) 
and the middle term according to rule 3. 

(6) But I distributes neither term and O dis- 
tributes its predicate only; I and O together, 
then, distribute but one term. 

(7) To draw a negative conclusion the premises 
must distribute two terms, the middle and 
the major, according to the foregoing. 

(8) Hence a conclusion from I and O is 
untenable. The same may be said of " OI." 

"II" considered. 



Rules of the Syllogism Explained 207 

(1) The I proposition distributes neither subject 
nor predicate, hence the premises " II " 
would distribute no term. 

(2) But the middle term must be distributed at 
least once according to rule 3. 

(3) Therefore no conclusion can be drawn 
from " II." 

A valid conclusion from " 00 " is impossible 

according to rule 5. 

(8) If one premise be particular the conclusion must 

be particular. Proof: The possible combinations 

conditioned by rule 8 are AI, AO, EI, EO, IO, II, 00. 

"AI" considered. 

(1) Proposition A distributes its subject, prop- 
osition I neither ; hence "AI " together 
distribute but one term. 

(2) According to rule 3 this one term must be 
the middle term. 

(3) The minor term must, therefore, be undis- 
tributed in the minor premise, and in con- 
sequence undistributed in the conclusion. 

(4) But this undistributed minor term is the sub- 
ject of the conclusion; hence said conclusion 
must be particular, as only particulars have 
an undistributed subject. 

"AO" and "EI" considered. 
Proof: 

(1) "AO" distribute two terms; so do "EL" 

(2) Both "AO " and " EI " must have negative 
conclusions according to rule 6. 



208 Mediate Inference — The Syllogism 

(3) A negative conclusion distributes its predicate 
which is the major term. 

(4) The major term and the middle term must 
be distributed in the premises. Rules 4 
and 3. 

(5) Thus the third term, which is the minor, 
cannot be distributed in the minor premise 
and, consequently, the minor cannot be 
distributed in the conclusion. 

(6) This necessitates a particular conclusion. 
Premises EO and OO, being negative, cannot yield a 

conclusion according to rule 5 ; similarly, neither can the 
particulars IO and II because of rule 7. 

5. THE DICTUM OF ARISTOTLE. 

Aristotle gives an axiom on which all syllogistic in- 
ference is based. Indeed from this fundamental prin- 
ciple the significant rules of the syllogism could be de- 
rived. The dictum is stated in this wise : " Whatever 
is predicated, whether affirmatively or negatively, of a 
term distributed may be predicated in the manner of 
everything contained under it." The following state- 
ments represent various ways of explaining this 
dictum : 

(1) Whatever is said of a term used in its fullest 
sense may likewise be said of that term when used only 
in a partial sense. 

(2) What is true of the whole is true of the part. 

(3) "What pertains to the higher class pertains also 
to the lower." Since this dictum is the basic principle 



The Dictum of Aristotle 209 

underlying the important rules of the syllogism, it is 
unnecessary to dwell longer upon it; because an 
explanation of the rules is, virtually, an explanation of 
the dictum. 

6. CANONS OF THE SYLLOGISM. 

The dictum of Aristotle is ostensibly a self-evident 
truth, and some logicians have put this truth in the form 
of three axiomatic statements which are known as the 
canons of the syllogism. These are as follows: 

(1) "Two terms agreeing with one and the same 
third term agree with each other." 

(2) " Two terms of wmich one agrees and the other 
does not agree with one and the same third term, do 
not agree with each other." 

(3) " Two terms both disagreeing with one and the 
same third term may or may not agree with each other." 

Making use of the symbols as explained on a previous 
page of this chapter, it will be seen that the first canon 
conforms to this syllogistic type: 

All M is G 

All S is M 



.". All S is G 
The two terms are S and G, while M is the third term. 

The attending symbolizations illustrate, respectively, the 
second and third canons: 

No M is G 
All S is M 



No S is G 



210 Mediate Inference — The Syllogism 

No M is G 
No S is M 
Conclusion indeterminate. 

7. THREE MATHEMATICAL AXIOMS. 

Analogous to the three canons treated in "6," there are 
certain mathematical axioms which are here stated : 

(i) "Things equal to the same thing are equal to 
each other." 

(2) "One thing equal to and the other thing not 

equal to the same third thing are not equal 
to each other." 

(3) "Things not equal to the same thing may or 

may not equal each other." 
Illustrations of the three axioms : 

(1) If x equals 5, and y equals 5, then x equals y. 

(2) If x equals 5, and y does not equal 5, then x 

does not equal y. 

(3) If x does not equal 5, and y does not equal 5, 

then x may or may not equal y. 

8. OUTLINE. 

Mediate Inference. 

(1) Inference and reasoning. 
Definitions. Middle term explained. 

(2) The analogy between the judgment and the syllogism. 

(3) Rules of the syllogism given. Eight in number. 

(4) Rules of the syllogism explained : 

Rule 1. Syllogistic symbols. 

Major, minor, and middle terms; how found. 
Fallacy of four terms. 



Outline 211 

Rule 2. Major and minor premises and conclusion, how 
determined. 

Logical arrangement. 

Reason for three propositions. 
Rule 3. Reason for omitting "ambiguous middle" from rule. 

Undistributed and distributed middle explained. 
Rule 4. Illicit major and minor explained and illustrated. 
Rule 5. Fallacy of two negatives. 
Rule 6. Fallacy of negative conclusion. 
Rule 7. Fallacy of two particulars. 
Rule 8. Fallacy of particular conclusion. 

(5) Aristotle's dictum. 

(6) Canons of the syllogism. 

(7) Mathematical axioms. 

9. SUMMARY. 

(1) Inference is a term used to denote a process as well as a 
product. As a process reasoning and inference are in reality 
synonomous terms. 

Inference is a thought process of deriving a judgment from 
one or two antecedent judgments. 

Mediate inference is inference by means of a middle term. 
Mediate inference makes use of three terms, two of which are 
compared with a third term as a standard. This third term is 
called the middle term. 

(2) The syllogism is the common mode of expression for 
mediate inference. 

(3) Valid syllogistic reasoning is conditioned by eight rules. 
The first and second relate to the composition of the syllogism; 
the third and fourth to the distribution of terms; the fifth and 
sixth to negative premises; the seventh and eighth to particular 
premises. 

(4) All syllogisms must have three terms: the major, the 
minor, and the middle. The middle term occurs twice in the 
premises but never appears in the conclusion. The minor term 
is always the subject, and the major term the predicate of the 
conclusion. The major term is usually broader than the minor. 

No conclusion can be drawn from four terms. To attempt 
this gives rise to the fallacy of four terms. 



212 Mediate Inference — The Syllogism 

All syllogisms must have three propositions, the major and the 
minor premises, and the conclusion. The major premise first 
and the minor second is the more logical arrangement, although 
the common conversational form is to use the minor premise 
first. 

Ambiguous middle amounts to the fallacy of four terms. 

Unless the middle term is distributed at least once in the 
syllogism, it fails to become a common standard. 

Distributing a term in the conclusion, without its being dis- 
tributed in its premise, is equivalent to asserting that, "What is 
true of a part is true of the whole." This error results in the 
fallacies of illicit major and minor. 

A conclusion from two negatives is impossible, because of the 
total exclusion of the middle term. 

Of two terms, if one is affirmed and the other denied of 
a third term, then they must be denied of each other; and, 
conversely, if two terms are to be denied of each other, one must 
be affirmed and the other denied of a given third term. This 
fundamental principle necessitates deriving a negative conclusion 
from two premises when one is negative. It, likewise, compels 
the converse of this. 

A valid conclusion from two particulars is untenable because of 
the two negative fallacies, or some fallacy relative to the 
distribution of terms. 

One particular premise forces a particular conclusion because 
of the fallacies of two negatives, two particulars, and illicit 
minor. 

(5) Aristotle's dictum simplified means, "What is true of the 
whole is true of the part." 

(6) The canons of the syllogism, three in number, are: 

(1) "Two terms agreeing with one and the same third 

term agree with each other." 

(2) "Two terms of which one agrees and the other does 

not agree with one and the same third term do not 
agree with each other." 

(3) "Two terms both disagreeing with one and the same 

third term may or may not agree with each other." 

(7) The foregoing canons may be stated as mathematical 
axioms. 



Illustrative Exercises 213 

10. ILLUSTRATIVE EXERCISES. 

(la) Make use of the proper symbols and indicate the three 
terms of each of the attending syllogisms : 
(1) All fixed stars twinkle, 
Vega is a fixed star, 



.*. Vega twinkles. 

(2) All men are rational beings, 
No tree is a rational being, 

.*. No trees are men. 

(3) All good citizens are law abiding, 
All good citizens vote, 

.*. Some who vote are law abiding. 

I recall that the three terms are the middle, the major and the 
minor, and that the "middle" does not occur in the conclusion, 
whereas the "major" is always the predicate and the "minor" the 
subject of the conclusion. The symbols M, G and S being the 
initial letters of middle, greater and smaller, I make use of 
these in designating the three terms, as the following will 
illustrate : 

M G 

(1) All fixed stars twinkle, 
S M 

Vega is a fixed star, 



S G 

.". Vega twinkles. 

"Twinkles" being the predicate of the conclusion is designated 
as being the major term by putting the letter G above it. Then 
"G" is placed above the term "twinkle" in the first premise. 

"S" is placed above the subject of the conclusion to indicate 
that it is the minor term. "S" is also placed above "Vega," the 
minor term, as found in the second premise. 

The remaining term, "fixed stars," must be the middle term, 
therefore I place "M" above it. The fact that "fixed star" does 
not occur in the conclusion verifies this. 



214 Mediate Inference — The Syllogism 

Using only the symbols, the syllogism takes this form: 
All M is G 
S is M 



S is G 



Using the symbols to represent the other syllogisms, we have 
(2) All G is M (3) All M is G 

No S is M All M is S 



.*. No S is G .*. Some S is G 

(lb) Indicate by symbols the three terms of the following 
syllogisms : 

(1) No trees are men, 

All rational beings are men, 



.*. No rational being is a tree. 

(2) All men have the power of speech, 
You are a man, 

.*. You have the power of speech. 

(3) Some men are wise, 
All men are rational, 

.'. Some rational beings are wise. 

(2a) Illustrate by syllogism the fallacy of undistributed 
middle. An easy way is to use the middle term as the predicate 
of two A premises. This yields the fallacy because an A propo- 
sition does not distribute the predicate. 

The illustration: distributed terms underscored. 

All true teachers are students, 



All scholars are students, 



All scholars are true teachers. 



(2b) Give two illustrations of undistributed middle. 
(3a) Give syllogistic illustrations of the fallacies of illicit 
major and minor. 



Illustrative Exercises 215 

Illicit Major. 

Use the middle term as the subject of an A proposition, and 
then as the predicate of an E proposition. This would necessitate 
a negative conclusion in which the major term is distributed. 
But the major term is not distributed in the major premise, hence 
the fallacy. 

Illustration in which the distributed terms are underscored: 
All men are mortal, 

No trees are men, 



No trees are mortal. 



Illicit Minor. 

To illustrate this fallacy one may use the middle term as the 
subject of two A premises. This would give an A conclusion in 
which the subject is distributed. But this same term is not dis- 
tributed in its premise because here it is used as the predicate of 
an A. Illustration: 

All earnest students study, 



All earnest students desire to succeed, 



,*. All who desire to succeed study. 



11. REVIEW QUESTIONS. 

(1) Distinguish between inference and reasoning. 

(2) Define inference. Mediate inference. 

(3) Illustrate the difference between mediate and immediate 
inference. 

(4) Explain by illustration the use of the middle term. 

(5) Exemplify the syllogism. 

(6) State the rules of the syllogism. 

(7) From the attending syllogisms select the three terms : 
(1) All patriotic citizens vote, ^ 

You are a patriotic citizen, 



You should vote. 






(2) No honest man would misrepresent, 

(but) John Smith did misrepresent, ■' t* Or , __,, M 

.*. John Smith is not honest. r- 

«> <Vtf /v| 



216 Mediate Inference — The Syllogism 

(8) Symbolize the foregoing syllogisms. 

(9) Illustrate by syllogisms the fallacy of four terms. 

(10) Indicate by circles that a valid conclusion cannot be 
drawn from four terms. 

(11) Why must a syllogism have three and only three 
propositions ? 

(12) Indicate how the three propositions of an argument may 
be designated. What is the logical arrangement? 

(13) Show that an ambiguous middle amounts to a fallacy of 
four terms. 

(14) Explain and illustrate undistributed middle, illicit major, 
illicit minor. 

(15) Exemplify the fallacies of question "14" by using circles. 

(16) Explain by circles why a conclusion cannot be drawn 
from two negatives. 

(17) Make clear that a negative conclusion must follow, if one 
premise be negative. 

(18) State and explain the principle which underlies the rule, 
"If the conclusion is negative one premise must be negative." 

(19) Prove by the process of elimination that no conclusion 
can be drawn from two particulars. 

(20) In a way similar to that of question "19" show that if 
one premise be particular the conclusion must be particular. 

(21) State and explain Aristotle's dictum. 

(22) State the canons of the syllogism. 

(23) Symbolize and explain by circles the three canons. 

(24) Illustrate the three mathematical axioms which the canons 
suggest. 

12. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Give an illustration of a valid conclusion being drawn 
from four terms. 

(2) Explain by circles the foregoing. 

(3) From three different business transactions, select the 
middle term of comparison. 

(4) Why should not those who are given to much which is 
argumentative, speak in syllogistic terms? 

(5) ("He is a man of high ideals, and you know him to be 



Questions for Original Thought and Investigation 217 

strictly honest, therefore you have no excuse for not voting 
for him." Recast this quotation with a view of making a logical 
syllogism. 

(6) Show by circles that there may be a vital difference 
between a syllogism of three terms and an equation of three 
terms. 

(7) Indicate by illustration that in conversational argumenta- 
tion the minor premise naturally comes first. 

(8) Show by circles the meaning of "indeterminate con- 
clusion." 

(9) Rule five states that no conclusion can be drawn from 
two negatives. Defend this rule in connection with the follow- 
ing syllogism, which seems to contain a valid conclusion: 

Any statement which is not true cannot be accepted, 
This statement is not true, 
/.It cannot be accepted. 

(10) If the conclusion is particular, must one premise be 
particular ? Explain. 



CHAPTER 12. 



FIGURES AND MOODS OF THE SYLLOGISM. 

1. THE FOUR FIGURES OF THE SYLLOGISM. 

By a figure of a syllogism is meant some particular 
arrangement of the three terms in the two premises. The 
conclusion is eliminated from this discussion, because in it 
the arrangement of the terms is constant, the major term 
always being used as the predicate of the conclusion and 
the minor as the subject. Using the symbols M, G and S, 
we find that there are four possible arrangements and, 
therefore, but four figures. These may be represented 
as follows: 

First figure Second figure Third figure Fourth figure 
M — G G — M M — G G — M 

S — M S— M M— S M— S 



S — G S— G S— G S — G 

No matter what the syllogism, if it is to be proved 
"logical" it should be made to fit one of the four figure- 
types. To be sure, it may fit the figure without being 
logical, but it cannot be strictly logical without fitting the 
figure. The following valid syllogisms conform to the 
four figures as will be seen by the symbolized terms : 

218 



The Four Figures of Syllogism 

M G 

First figure : All men are mortal, 
S M 

Socrates is a man, 
S G 

.'. Socrates is mortal. 

M — G 

S — M 



219 





S — G 




G M 


figure: 


All good citizens love their country, 




S M 




No criminal loves his country, 




S G 


.' 


. No criminal is a good citizen. 




G — M 




S — M 



S — G 

M G 

Third figure : All good citizens are law abiding, 

M S 
All good citizens vote, 

S G 

.*. Some who vote are law abiding. 
M — G 
M — S 

S — G 



220 Figures and Moods of the Syllogism 

G M 

Fourth figure : Some teachers are fair minded, 

M S 

All who are fair minded are just, 
S G 

.". Some just persons are teachers. 
G — M 
M — S 



S — G 
Here, then, are the types that represent all the syllogisms 
which mediate inference may use. Logic recognises no 
other. Since every successful student of logic must be 
familiar with the four figures, the following may be used 
as a suggestive aid to reproducing the figures at will : 
First. It is easy for any one to remember this syllogism : 
All men are mortal, 
Socrates is a man, 
. ' . Socrates is mortal. 
In fact, it comes down to us from the time of Aristotle, 
and is therefore a patriot of many generations to whom 
the faithful should touch their hats. Let us, then, be 
ready to reproduce this syllogism with automatic pre- 
cision, since it will enable us to know at once the position 
of the terms in the first figure. Second. Converting the 
terms of the major premise of the first figure gives the 
second figure, as, e. g. : 

First figure. Second figure. 

M — G (Convert) G — M 

S — M S — M 



The Four Figures of Syllogism 221 

Third. Converting the terms of the minor premise of the 
first figure gives the third figure, as, e. g. : 

First figure. Third figure. 

M — G M — G 

S — M (Convert) M — S 



S — G S — M 

Fourth. Converting the terms of both the major and 
minor premises of the first figure gives the fourth, as, e. g. : 

First figure. Fourth figure. 

M — G (Convert) G — M 
S — M (Convert) M — S 



S — G 



To summarize : The second, third and fourth figures may 
be derived from the first. Converting the major premise 
of the first figure gives the second figure; converting the 
minor premise gifues the third figure; and converting both 
premises gives the fourth figure. 

2. THE MOODS OF THE SYLLOGISM. 

By the mood of a syllogism is meant some particular 
arrangement of the propositions which compose the syllo- 
gisms. "Mood" stands for an arrangement of the propo- 
sitions, while "figure" represents an arrangement of the 
terms in any syllogism. 

Combining any three of the four logical propositions 
gives a mood, as, e. g., (1) E (2) A (3) E 

A II 

E I O 



222 Figures and Moods of the Syllogism 

are moods. The first one has an E proposition for the 
major premise, an A for the minor and an E for the 
conclusion. This syllogism represents the first mood given 
above : 

E No men are trees, 

A All Americans are men, 

E .'. No Americans are trees. 

It would not be difficult to determine by actual experi- 
ment, just how many moods could be formed, and of 
these, how many would admit of valid conclusions. It 
may be seen that there are sixty- four permutations of the 
four logical propositions, taken three at a time. These 
are in part: 



(I) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


A 


A 


A 


A 


A 


A 


A 


A 


A 


A 


A 


A 


E 


E 


E 


E 


A 


E 


I 


O 


A 


E 


I 






(9) (io) (ii) (12) (13) (14) (15) (16) 
AAAAAAAA 

-I I I I O O O O 

A E I O A E I O 

And so the permutations could be continued. Substituting 
E for the major premise of the above group would give 
another group of sixteen, while a like substitution of I and 
O would result in two more groups , sixteen in each. This 
gives sixty-four in all.* 



The student may be sufficiently interested to complete the list. 



Testing the Validity of the Moods 223 

3. TESTING THE VALIDITY OF THE MOODS. 

In order to put the moods to good use, it is necessary to 
ascertain which ones yield a valid conclusion in any figure. 
If each were valid in all of the four figures, there would 
be 256. But it is obvious that such is not the case. 

Referring to the sixteen permutations given above, we 
find that the "negative-conclusion" rule makes invalid 
2 > 4> 5 j 7> I0 > I2 j x 3 an d 15; whereas the rule for par- 
ticulars throws out 9 and 14. This leaves the following 
as the probable valid moods in one or more of the figures : 
1, 3, 6, 8, 11, 16. But to be certain of this the investiga- 
tion must be continued. The mood A has stood the test 

A 
A 
of the rules for negative and particular conclusions ; now 
let us test this mood from the standpoint of the distribu- 
tion of terms, using it in all four figures : 

First Second Third Fourth 

A M — G G — M M — G G — M 

A S — M S — M M — S M — S 



A S — G 



As an A proposition distributes its subject only, we 
underscore the subject of each proposition in all the 
figures. (This underscoring is a simple way to indicate 
distribution.) 

We now find that the mood is valid in the first figure, 
because the middle term is distributed at least once; 



224 Figures and Moods of the Syllogism 

namely, in the major premise, and there is no term dis- 
tributed in the conclusion which is not already distributed 
in the premise where it occurs. On the other hand, the 

A 
mood A is invalid in the second, because of "undistributed 

A 
middle/' and invalid in the third and fourth, because S is 
distributed in the conclusion but not distributed in the 
premise where it occurs (illicit minor). 
Let us try All in the four figures : 

A M — G G — M M — G G — M 

IS— M S — M M — S M — S 



IS— G S — G S — G S — G 

We underscore the subject of the A proposition in each 
of the four figures. As I distributes neither subject nor 
predicate, no other term should be underscored. It is 

A 
now evident that I is not valid in figures two and four, 

I 
because in both figures the middle term is undistributed 
(undistributed middle). 

In a like manner all the other moods might be tested. 
Logicians, who have done this, have found 24 to be 
valid. Five of these have weakened conclusions; i. e., a 
particular conclusion when it could just as well be uni- 

A 
versal. E illustrates this as the conclusion could be E. 
O 



Testing the Validity of the Moods 225 

This syllogism exemplifies the weakened conclusion : 

A All trees grow, 

E No sticks are trees, 

O .'. Some sticks do not grow. 

This conclusion is true, since "some" means "some at 
least." Yet the conclusion is weak, because there is 
nothing to interfere with the broader and stronger con- 
clusion that, "No sticks grow." There are, therefore, 
only 19 valid and serviceable moods. These are as 
follows : 





(1) 


(2) 


(3) 


(4) 


(5) 


(6) 




A 


E 


A 


E 


— 


-1 


First figure 


A 


A 


I 


I 


— 


-I 




A 


E 


I 


O 


— 


-J 




E 


A 


A 


E 





-\ 


Second figure 


A 


E 


O 


I 


— 




E 


E 


O 


O 


— 


-J 




A 


I 


A 


E 


O 


E l 


Third figure 


A 


A 


I 


A 


A 


1 




I 


I 


I 


O 


O 


oj 




A 


A 


I 


E 


E 


-1 


Fourth figure 


A 


E 


A 


A 


I 


-!■ 




I 


E 


I 


O 


O 


-J 



14 



19 



Of these nineteen moods it is not much of a tax to 
A 
remember that A is valid only in the first figure ; whereas 
A 



226 Figures and Moods of the Syllogism 

E A 

A is valid in the first and second figures ; I in the first 
E I 

E 
and third; while I is valid in all. This knowledge, 

O 
however, should be used only as one would employ the 
answers in arithmetic. Testing the validity of a mood in 
the four figures is an exceedingly valuable thought- 
exercise, which a knowledge of the final result might 
easily vitiate. It is, no doubt, best to test the value of 
any mood without such knowledge, and then compare the 
result by referring to the foregoing list of valid moods. 
It is not always wise to work with the answer in mind, 
yet it is most satisfying to know of a certainty that 
one's reasoning has led to a truth which others have 
verified. 

4. SPECIAL CANONS OF THE FOUR FIGURES. 

As a deductive exercise in clear, logical thought, the 
indirect proof involved in establishing certain principles 
underlying the four figures, is of immense value. On no 
account should this section be omitted. The mere fact 
that it appears to be a difficult section is proof positive 
that the student is in need of just such exercises. 

Canons of the first figure. 

( i ) The minor premise must be affirmative. 

(2) The major premise must be universal. 
Problem: The minor premise must be affirmative. 



Special Canons of the Four Figures 22J 

Data: Given the form of the first figure, which is, 
M — G 
S — M 



S — G 

Proof: (1) If the minor premise is not affirmative 
then it must be negative ; because affirmative and negative 
propositions, being contradictory in nature, admit of no 
middle ground. 

(2) If the minor premise is negative, the conclusion 
must be negative ; for the reason that a negative premise 
necessitates a negative conclusion. 

(3) If the conclusion is negative then its predicate, G, 
must be distributed; since all negatives distribute their 
predicates. 

(4) If the predicate of the conclusion, which is the 
major term, is distributed, then it must be distributed in 
the premise where it occurs, which is the major premise; 
for any term which is distributed in the conclusion must 
be distributed in the premise where it occurs. 

(5) If the major term, which is the predicate of the 
major premise, is distributed, then the major premise 
must be negative; because only negatives distribute their 
predicates. 

(6) The result of this argument, then, gives two nega- 
tive premises, and we know from rule 3 that a conclusion 
from two negatives is untenable. 

(7) Since the minor premise cannot be negative, it 
must be affirmative. 

Problem: To prove that the major premise must be 
universal. 



228 Figures and Moods of the Syllogism 

Data: Given the form of the first figure: 
M — G 

S — M 



S — G 
Proof: (i) The predicate of the minor premise, M, 
which is the middle term, is undistributed; because no 
affirmative proposition distributes its predicate. 

(2) The middle term must be distributed in the major 
premise; since in any syllogism the middle term must be 
distributed at least once. 

(3) As the middle term, M, used as the subject of the 
major premise, must be distributed, then the major 
premise must be universal; because only universals 
distribute their subjects. 

Epitome. 

In the first figure, the minor premise must be affirma- 
tive, since making it negative necessitates making the 
major premise negative also; the major premise must be 
universal in order to distribute the middle term at least 
once. 

Special canons of the second figure. 

( 1 ) One premise must be negative. 

(2) The major premise must be universal. 
Problem: To prove that one premise must be negative. 
Data: Given the form of the second figure: 

G — M 
S — M 

S — G 



Special Canons of the Four Figures 229 

Proof: (1) The middle term, M, is the predicate of 
both premises. 

(2) The middle term must be distributed at least once, 
according to rule 3. 

(3) Hence one premise must be negative; since only 
negatives distribute their predicates. 

Problem: To prove that the major premise must be 
universal. 

Data: Given the form of the second figure: 
G — M 
S — M 



S — G 
Proof: (1) As one premise must be negative, it fol- 
lows that the conclusion must be negative according to 
rule 6. 

(2) If the conclusion is negative, then its predicate, 
G, the major term, must be distributed ; since all negatives 
distribute their predicates. 

(3) When distributed in the conclusion, the major 
term, G, must also be distributed in the major premise, 
where it is used as the subject. See rule 4. 

(4) Hence the major premise must be universal; for 
only universals distribute their subjects. 

Epitome. 

In the second figure one premise must be negative in 
order to distribute the middle term at least once; and the 
major premise must be universal that the major term, 
which is distributed in the conclusion, may be distributed 
in the premise where it occurs. 



230 Figures and Moods of the Syllogism 

Canons of the third figure. 

(1) The minor premise must be affirmative. 

(2) The conclusion must be particular. 

Problem: To prove that the minor premise must be 
affirmative. 

Data: Given the form of the third figure, which is, 

M — G 

M— S 



S — G 
Proof: ( 1 ) Suppose the minor premise were negative, 
then the conclusion would have to be negative, and this 
would distribute the predicate G. 

(2) A distributed predicate would necessitate its being 
distributed in the major premise. 

(3) But G, being the conclusion of the major premise, 
could be distributed only by a negative proposition. 

(4) This would result in two negatives; therefore no 
conclusion could be drawn, if the minor premise were 
negative. 

Problem: To prove that the conclusion must be 
particular. 

Data: Given the form of the third figure: 

M — G 

M— S 



S — G 

Proof: (1) The minor term, which is the predicate 
of the affirmative minor premise, is undistributed ; because 
no affirmative distributes its predicate. 

(2) If undistributed in the premise, then the minor 



Special Canons of the Four Figures 231 

term must remain undistributed in the conclusion, where 
it is used as the subject. 

(3) The conclusion must, then, be particular; since all 
universals distribute their subjects. 

Epitome. 

In the third figure, unless the minor premise be af- 
firmative, there can be no conclusion; since a negative 
minor would necessitate a negative major. An affirma- 
tive minor compels a particular conclusion, in order that 
the minor term, in the conclusion, may remain undis- 
tributed. 

Canons of the fourth figure. 

(1) If the major premise is affirmative, the minor 
premise must be universal. 

(2) If the minor premise is affirmative, the conclusion 
must be particular. 

(3) If either premise is negative, the major must be 
universal. 

Problem: To prove that if the major is affirmative, 
the minor must be universal. 
Data: Given the form of the fourth figure: 

G — M 

M— S 



S — G 

Proof: (1) If the major premise is affirmative, then 
its predicate which is the middle term, M, is undis- 
tributed ; for no affirmative distributes its predicate. 

(2) The middle term must then be distributed in the 
"minor" according to rule 3. 



232 Figures and Moods of the Syllogism 

(3) Then the "minor" must be universal; since only 
universals distribute their subjects. 

Problem: To prove that if the minor is affirmative, 
the conclusion must be particular. 

Data: Given the form of the fourth figure: 
G — M 
M— S 



S — G 
Proof: (1) If the minor premise be affirmative, then 
S, its predicate, must be undistributed ; because no affirma- 
tive distributes its predicate. 

(2) Since S is undistributed in the minor premise, it 
must remain undistributed in the conclusion where it is 
used as the subject. 

Problem: To prove that if either premise is negative, 
the major must be universal. 

Data: Given the form of the fourth figure: 
G — M 
M— S 



S — G 
Proof: (1) If one of the premises is negative, then 
the conclusion must be negative according to rule 6. 

(2) If the conclusion is negative, then the predicate, G, 
must be distributed. 

(3) If G is distributed in the conclusion, it must be 
distributed in the major premise. 

(4) The major premise must be universal ; as G is used 
as its subject, and only universals distribute their subjects. 

Epitome. 



Special Canons of the Four Figures 233 

In the fourth figure, if the "major" is affirmative, the 
"niMor" must be universal in order to distribute the mid- 
dle term. If the minor is affirmative, the conclusion must 
be particular; otherzvise the fallacy of illicit minor would 
result. If either premise is negative, the major must be 
universal to avoid the fallacy of illicit major. 

5. SPECIAL CANONS RELATED. 

After a particular mood has been tested in the regular 
way, it has been intimated that the student may refer to 
the tabulated list of valid moods to ascertain, with a cer- 
tainty, the validity of his reasoning. This is equivalent to 
referring to the answers in arithmetic; for if the student 
is unable to find the mood in the figure in which he has 
proved it valid, then he knows that he has made some mis- 
take in his reasoning. A second check, though not abso- 
lute, is to recall the special canons of section four. If, 

A 

for example, our reasoning has led us to believe that E 

E 
is valid in the first figure, we may recall that the minor 

premise of the first figure must be affirmative and there- 
fore AEE cannot be valid. 

A few suggestions relative to memorizing the special 
canons may not be out of place. The two canons of the 
first figure must be committed, and then it may be re- 
membered that the second figure is the negative figure of 
logic. Other figures may yield a negative conclusion, but 
the second must yield a negative conclusion. Since a 
negative conclusion necessitates a negative premise, it 
follows that the second figure must always appear with 



234 Figures and Moods of the Syllogism 

one premise negative. The other canon which pertains to 
the major premise is the same as the "major premise" 
canon of the first figure. 

The third figure is the particular figure of logic. Other 
figures may yield particular conclusions, but the third 
must do so. This helps us to remember the canon that 
the conclusion of the third figure must be particular. 
The other canon which relates to the minor premise is 
the same as the "minor premise" canon of the first figure. 
The canons of the fourth figure are in reality a summary 
of the canons of the other three figures. 

6. MNEMONIC LINES. 

As a device for remembering the 19 valid moods, the 
logicians of an earlier day originated a combination of 
coined words which, though rather unscientific, may be 
easily committed to memory. Since, however, it is of 
much more value to test the moods by means of the gen- 
eral rules of the syllogism than it is to try to remember 
these moods, the mnemonic lines are of slight value. 
They are treated here merely as an item of historical 
interest. 

( 1 ) Barbara, Celarent, Darii, Ferioque prioris ; 

(2) Cesare, Camestres, Festino, Baroko, secundae; 

(3) Tertia, Darapti, Disamis, Datisi, Felapton. 
Bokardo, Ferison, habet; Quarta insuper addit 

(4) Bramantip , Camenes, Dimaris, Fesapo, Fresison. 
The only letters in these lines which mean nothing are 

1, n, r, t and small b and d; all the others have a sig- 
nification. For example, the vowels of the italicized 



Mnemonic Lines 235 

words signify the various valid moods, as e. g., the first 
line indicates the moods AAA, EAE, All, EIO. The 
Latin words, printed in ordinary type, are intended to 
make evident that the moods indicated by the artificial 
italicized words of the first line, belong to the first figure ; 
that the moods of the next four words, belong to the 
second figure ; while the third figure includes the next six, 
and the fourth figure the last five. It is now seen that 
Festino, for example, stands for that mood of the second 
figure which has an E for its major premise, an I for its 
minor premise, and an O for its conclusion. 

The first figure was called by Aristotle the perfect 
figure, whereas the second and third were the imperfect 
figures. The fourth figure was given no place in the 
works of Aristotle; its discovery is credited to Galen, a 
celebrated teacher of medicine of the second century. 
According to Aristotle, the first figure is the most service- 
able and the most convincing and, therefore, as a final 
test of their validity, the moods of the other figures 
should be changed to the first. This process in logic is 
termed Reduction. In this reduction of the imperfect 
figures to the perfect, the capital letters of the artificial 
words, together with s, p, m, and k, have a definite 
meaning. The capital letters indicate that certain moods 
of the imperfect figures can be reduced to the correspond- 
ing moods of the first figure; e. g., Festino (eio) of the 
second figure, Felapton (eao) of the third figure, and 
Fesapo (eao) of the fourth figure may all be reduced to 
Ferio (eio) of the first figure. This is known because F 



236 Figures and Moods of the Syllogism 

is the initial letter of each word, j signifies that the prop- 
osition denoted by the preceding vowel is to be converted 
simply. To illustrate: s in Fesapo means that the major 

E 
premise E of the mood A of the fourth figure must be 

O 
converted simply in order to change the mood to Ferio 
of the first figure, p indicates that the proposition repre- 
sented by the vowel which precedes p must be converted 
by limitation (per accidens). m (mutare) makes evi- 
dent that the premises are to be interchanged, the major 
of the old becoming the minor of the new, and the minor 
of the old becoming the major of the new. k denotes that 
the mood, such as Baroko, must be reduced by a special 
process known as indirect reduction. These directions 
may now be followed as illustrative of the process of 
reduction. 

A 
(1) Given: A syllogism in Darapti A 

I 
M G 

A All true teachers are just, 

M S 

A All true teachers are sympathetic, 
S G 

I .'. Some sympathetic persons are just. 

A 
The symbols indicate that the mood is A or is in 

I 
Darapti and that this mood is used in the third figure. 



Mnemonic Lines 237 

A 
Problem: To reduce A of the third figure to some 
I 
mood of the first figure. 

Process: D, being the initial letter of Darapti, sug- 
gests that its mood must be reduced to one indicated by a 
word of the first figure whose initial letter is D. This 

A 

mood is in Darii, or is I. 

I 

The p in Darapti indicates that the proposition repre- 
sented by the preceding vowel must be converted by 
limitation. This proposition is the minor premise; con- 
verting it by limitation gives : "Some sympathetic persons 
are true teachers." As there are no other significant let- 
ters the reduction is complete and we have this : 

M G 

A All true teachers are just, 

S M 

I Some sympathetic persons are true teachers, 

S G 

I .'. Some sympathetic persons are just. 

A 
The symbolization indicates that the mood is I of the first 

I 
figure, or is in Darii. 

A 
(2) Given: A syllogism in Camestres E 

E 



238 Figures and Moods of the Syllogism 

G M 

A All true teachers are just, 

S M 

E No one who shows partiality is just, 

S G 

E .'. No one who shows partiality is a true teacher. 

The symbols show that the mood is AEE of the second 

figure or in Camestres. Judging from the initial letter C, 

the mood in Camestres must be reduced to the mood in 

E 
Celarent A. 
E 
The letter m between a and e indicates that the major 
and minor premises of the given syllogism must be 
interchanged. The letters following both e's suggest that 
the minor premise and the conclusion of the syllogism 
must be converted simply. 

This is the resulting syllogism: 

M G 

E No just person shows partiality, 
S M 

A All true teachers are just persons, 

S G 

E .'. No true teacher shows partiality. 
E 
Here, then, is the A of the first figure or the mood in 

E 
Celarent. 

According to the ancient theory, reduction is necessary 
as a matter of final and absolute proof that the conclusion 



Mnemonic Lines 239. 

follows from the given premises. But, as this claim has 
been satisfactorily refuted by modern logicians, we need 
not give more space to the process. The meaning of k, 
as related to "indirect reduction/ 3 is explained in most of 
the earlier works on logic. See Hyslop, page 193. 

7. RELATIVE VALUE OF THE FOUR FIGURES. 

The first figure. 

The first figure is known as the perfect figure ; because 
it is the only one which proves all of the four logical 
propositions. Recalling the moods of the first figure 
makes this evident : 

A E A E 

A A I I 

A E I O 

It is likewise the more natural figure ; because it is the 

only one which uses both the subject and predicate of 

the conclusion in the same relative places as they appear 

in the premises. Symbolizing the figure makes this 

apparent : 

M — G 

S — M 

S — G 

The first figure, being the only figure which proves a 

"universal affirmation" (A), is used most by the scientist; 

as the object of science is to establish universal affirmative 

truths. 

The second figure. 

As the second figure conditions negative conclusions 
only, it is called the figure of disproof, or the exclusive 



240 Figures and Moods of the Syllogism 

figure. It is easy to see how negative conclusions may be 
used to narrow the inquiry down to one definite theory. 
For example, suppose it is desired to ascertain which boy 
of the five broke the window; by a series of deductions 
the teacher may be able to prove that the culprit is not A, 
not B, not C and not D ; hence the guilty one must be E. 
This figure is virtually the one used in diagnosing most 
diseases. 

The third figure. 

The third figure admits of particular conclusions only, 
and in consequence is of little value to the scientist. Since, 
however, the easiest way to contradict a universal affirma- 
tive (A) or a universal negative (E), is to prove the 
truth, respectively, of a particular negative (O) and a 
particular affirmavite (I), it follows that the third figure 
serves a purpose. 

The fourth figure. 

This figure is so nearly like the first that it is of little 
value; in fact, it may be changed to the first by simply 
interchanging the major and minor premises. Some 
authorities refuse to recognize the fourth figure. 

8. OUTLINE. 

Figures and Moods of the Syllogism. 

(1) The four figures of the syllogism. 

Definition — symbolization 
Illustrations — device for remembering. 

(2) The moods of the syllogism. 

Twenty-four valid. 

(3) Testing the validity of the moods. 

Application of the general rules of the syllogism. 
Weakened conclusion — five. 



Summary 241 

Nineteen useful moods. 
A thought exercise. 

(4) Special canons of the four figures. 

Proof of the two canons of the first figure. 
" " " " " " " second figure. 

" " " " " " u third figure. 

" " " three " " " fourth figure. 

(5) Special canons related. 

Used as checks. 

(6) Mnemonic lines. 

Their use explained. 
Reduction. 

(7) Relative value of the four figures. 

9. SUMMARY. 

(1) By a syllogistic figure is meant some particular arrange- 
ment of the three terms in the two premises. 

This arrangement yields four figures which are designated by 
the position of the middle term. 

To be logical, any syllogism must conform to one of the four 
figures. The first figure is suggested by the position of the 
terms of the "Socrates is mortal" syllogism. The second is 
derived by converting the major premise of the first; while the 
third figure results from converting the minor premise of the 
first, and the fourth by converting both major and minor of the 
first. 

(2) By a mood of a syllogism is meant some particular ar- 
rangement of the propositions which compose it. 

There are 64 moods but only 24 are valid. 

(3) The validity of the various moods may be tested by 
applying to them the rules of the syllogism. No mood is valid 
if it violates any one of the eight rules. 

A "weakened conclusion" is a particular conclusion which 
could just as well be universal. 

Of the 24 valid moods five have weakened conclusions. This 
leaves but 19 useful moods. 

Testing the validity of the various moods in the four figures 
is a most valuable thought exercise. 

(4) The deductive exercise involved in establishing certain 



242 Figures and Moods of the Syllogism 

special canons of the four figures is of immense value and 
should not be omitted. 

In the first figure it may be proved (1) that the minor premise 
must be affirmative; since making it negative necessitates making 
the major premise negative,, and no conclusion can be drawn 
from two negatives; (2) that the major premise must be 
universal in order to distribute the middle term at least once. 

In the second figure it may be proved (1) that one premise 
must be negative in order to distribute the middle term; (2) 
that the major premise must be universal in order to distribute 
its subject, which is distributed in the negative conclusion where 
it appears as the predicate. 

In the third figure it may be proved (1) that the miner 
premise must be affirmative in order to prevent the "two negative" 
fallacy; (2) that an affirmative minor necessitates a particular 
conclusion, because the minor term in the conclusion must 
remain undistributed. 

In the fourth figure it may be proved (1) that if the major is 
affirmative, the minor must be universal in order to distribute 
the middle term; (2) that if the minor is affirmative, the con- 
clusion must be particular in order to avoid committing the 
fallacy of illicit minor; (3). that if either premise is negative, 
the major must be universal to avoid the fallacy of illicit major. 

(5) A knowledge of the special canons is helpful in that it 
may be used to check fallacious reasoning. 

(6) Certain mnemonic lines were used by the Schoolmen as 
an aid in recalling the nineteen valid moods, and also as a 
suggestive device to aid in the process known as Reduction. 

The process of reduction is merely a matter of changing to the 
first figure the moods of the other figures. This process is no 
longer thought to be necessary. 

(7) The first figure, called the perfect figure, is the one used 
most by scientists, as it is the only figure which proves a uni- 
versal affirmative truth. The second figure is the negative, or 
figure of disproof, and is used mainly for the purpose of elimi- 
nating all the conditions of the inquiry save one. The third 
figure serves a purpose in affording an easy way to contradict a 
universal assertion; this is the figure of particulars. The fourth 
figure, because it so closely resembles the first, is of little value. 



Illustrative Exercises 243 

10. ILLUSTRATIVE EXERCISES. 

Question la. By making use of the rules for negatives and 
particulars, test the validity of the following moods : 

A A 

1 I A 
A A I 

Answer: The first mood has the negative O as its major 
premise, and the affirmative A as its conclusion; the mood is 
thus invalid; because a negative premise necessitates a negative 
conclusion according to rule 6. 

The second mood contains the particular proposition I as its 
minor premise, and thus should have a particular conclusion 
according to rule 8. But the conclusion A is universal and, 
therefore, the mood is invalid. 

The premises of the third mood are universal and the con- 
clusion particular. The mood, however, is valid, because rule 8 
does not work both ways, as does rule 6. When a universal 
can just as well be drawn, then the particular becomes a 
weakened conclusion. 

(lb) Using the rules for negatives and particulars, test the 
A E E 
validity of the following : A O A . 
E O O 

(2a) Paying no regard to "figure," derive as many conclusions 
as possible from the following sets of premises: 

E A 
I E 

Answer: j . The major piemise of this mood, being negative, 

necessitates a negative conclusion, according to rule 6, and the 
minor premise, being particular, compels a particular conclusion, 
according to rule 8. Since the conclusion must be negative and 
particular, then O is the only one which can be drawn. The 

E 
completed mood is I. 

O 

P . This mood must have a negative conclusion, because the 
minor premise is negative; this would necessitate either E or O; 



244 Figures and Moods of the Syllogism 

but O as a conclusion would be, in this case, a weakened one; 
since E distributing both terms would necessarily distribute the 
minor; which fact would permit the minor to be distributed in 
the conclusion. Thus the conclusion could just as well be 

A 
universal as particular. The completed mood is E. 

E 
(2b) From the following sets of premises derive as many 
conclusions as possible paying no attention to figure : 
E A O 
AAA. 
(3a) Making use of all the general rules of the syllogism, 

A 
test the validity of the following mood in all the figures : A. 

I 
12 3 4 

Answer : A M — G G — M M — G G — M 

A S — M S— M M— S M— S 



I S — G S — G S — G S — G 

An underscored symbol indicates a distributed term. Since A 
distributes its subject, the subjects of both premises are under- 
scored in all the figures. No term is underscored in the con- 
clusions; since I distributes neither term. In the first figure the 
middle term is distributed in the major premise, and no term is 
distributed in the conclusion. Since both premises are affirmative, 
the rules for negatives are not applicable; and as a particular 
may be drawn from two universals, if there is no violation of 
the rules for distribution, this mood seems to be valid in the 
first figure. It is, however, a weakened conclusion; since an A 
could just as well be drawn. The mood is invalid in the second 
figure because of undistributed middle, but valid in (both the 
third and fourth ; since in both cases the middle term is distributed 
at least once. 

(3b) Determine the 'validity of the attending moods in all 

I A E 
the figures giving reasons : A O A 

I O O 



Review Questions 245 

11. REVIEW QUESTIONS. 

(1) Define a logical figure and illustrate by means of some 
ordinary syllogistic argument. 

(2) Symbolize the four figures and give suggestions for 
remembering them. 

(3) Write syllogisms which illustrate each of the four 
figures. 

(4) Define mood as it is used in logic. Illustrate. 

(5) How many moods are valid? 

(6) Explain by illustration a "weakened conclusion." 

A E 

(7) Test the validity of E in the third figure; of I in the 
third. E O 

(8) Independent of all helps, prove the truth of the canons of 
the first figure. 

(9) In a similar way prove the canons of the second, third 
and fourth figures. 

(10) So far as testing arguments is concerned, what use may 
be made of the special canons of the syllogism? 

(11) Offer a few suggestions for remembering the special 
canons. 

(12) Why did Aristotle attach so much importance to reduc- 
tion in logic? 

(13) Justify calling the first figure the "perfect figure," and the 
others the "imperfect figures." 

(14) Treat of the relative value of the four figures. 

(15) Show by illustration that the second figure is the ex- 
clusive figure. 

E O I 

(16) Test the following moods in all the figures: I A A 

A O I 
AEEAAEAAA 
E I A E I E O A I. 
O O O O E I I I I 

12. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 

TIGATION. 

(1) Give an illustration of a syllogism in the fourth figure 
which might just as well be written in the first figure. 



246 Figures and Moods of the Syllogism 

(2) May a syllogism, which is invalid in the fourth figure, be 
made valid by writing it in the form of the first figure? Prove it. 

(3) Show why it is impossible to apply all the rules of the 

(4) Show the difference between a direct and an indirect 
to the figures. 

(4) Show the difference between a direct and an indirect 
proof. A 

(5) Show that A is valid in the first figure when the major 

O 
premise (A) is co-extensive. 

(6) The third figure is known as the figure of particular 
conclusions. Why should not the second canon of that figure be, 
"One premise must be particular" rather than "The conclusion 
must be particular?" 

(7) Show that there is some ground for thinking that, as a 
final test, moods in the other figures should be reduced to the 
first. 

(8) Illustrate the fact that the second figure is the figure of 
disproof; whereas the third is the figure of contradictions. 

(9) "To be logical a syllogism must conform to one of the 
four figures, but this does not mean, necessarily, that all argu- 
ments must conform to some figure." Explain this. 



CHAPTER 13. 

INCOMPLETE SYLLOGISMS AND IRREGULAR ARGUMENTS. 

1. ENTHYMEME. 

An enthymeme is a syllogism in which one of the three 
propositions is omitted. 

Suppressing the major premise gives an enthymeme of 
the first order; whereas if the minor premise be sup- 
pressed, the enthymeme becomes one of the second order; 
while omitting the conclusions gives an enthymeme of the 
third order. 
Illustrations: 

Complete syllogism. 

All true teachers are just, 
You are a true teacher, 

(Hence) You are just. 

Enthymeme of first order; major premise omitted. 



You are a true teacher, 
(Hence) You are just. 
Enthymeme of second order; minor premise omitted. 

All true teachers are just, 



(Hence) You are just. 
Enthymeme of the third order; conclusion omitted. 
All true teachers are just, 
(And) You are a true teacher, 



247 



248 Incomplete Syllogisms 

To argue in terms of the complete syllogism is the 
unusual, not the usual method. We have a way of ab- 
breviating our remarks; expressing only the necessary 
and leaving the obvious to be taken for granted. Thus 
the enthymeme becomes the natural form of expression. 
But the mere fact that a part of the argument is omitted, 
makes it more essential for the student to think clearly 
and with careful continuity, that no error may intrude 
itself. 

Probably the most common enthymemes are those of 
the first order. This may be explained by the fact that 
the major premise is usually the most universal of the 
three propositions, and, in consequence, the one which 
would be the most generally understood. The following 
represent enthymemes of this order, gleaned from the 
ordinary conversation of ordinary people : 

( 1 ) "Your beets won't grow, because you are plant- 

ing them in the wrong time of the moon." 

(2) "You, being a member of the Sunday School, 

should be ashamed of such language." 

(3) "Being the son of your father, you ought to 

have some pride in this matter." 

(4) "We are going to have an open winter, because 

I have observed that the hornets' nests are 
near the ground." 

(5) "You had better put in lots of coal, for I have 

noticed that the squirrels have gathered in 
more nuts than usual." 
Judging from these enthymemes, it would seem to be 
more natural to assert the conclusion and follow this by 



Enthymeme 249 

a reason in the form of a minor premise, leaving the 
major to the intelligence of the auditor. 

The enthymeme of the second order occurs only in- 
frequently, since it seems to be an unnatural mode of 
expression, though sometimes it appears to lend emphasis 
to the conclusion; e. g., "All untrustworthy boys come to 
a bad end, and I predict that you will come to a bad end." 

Enthymemes of the third order are commonly used for 
the sake of emphasis, as the following make evident : 

(1) "No business man wants an indolent boy, and 

you are indolent." 

(2) "All successful teachers are interested in their 

work, and you plan to be a successful teacher." 

(3) "Humility is a sign of greatness, and Lincoln 

possessed this quality." 

2. EP1CHEIREMA. 

An epicheirema is a syllogism in which one or both of 
the premises is an enthymeme. To put it in another way : 
An epicheirema is a syllogism in which one or both 
of the premises is supported by a reason. 

When one premise is an enthymeme the syllogism is 
termed a single epicheirema ; whereas when both premises 
are enthymemes it becomes a double epicheirema. 
Single epicheirema. 

All men are mortal, because all men die, 
Socrates was a man, 
.". Socrates was mortal. 
Double epicheirema. 

All men are mortal, because all men die, 



250 



Incomplete Syllogisms 



Socrates was a man, because he was a rational animal, 

.'. Socrates was mortal. 

It is obvious that supporting each premise with a reason 
lends strength to the argument. This justifies the use of 
the epicheirema. 



3. POLYSYLLOGISM. 

A poly syllogism is a series of syllogisms in which the 
conclusion of a preceding syllogism becomes a premise 
of a succeeding one. 

The syllogism in the series whose conclusion becomes a 
premise of the succeeding syllogism is termed a pro- 
syllogism; while the syllogism which uses as one of its 
premises the conclusion of the preceding syllogism is 
called an episyllogism. 
Illustrations. 

fA quadruped is an animal/ 
A dog is a quadruped, >Prosyllogism 
Polysyllogism\ . ' . A dog is an animal. 1 

Fido is a dog, \-Episyllogism 

. Fido is an animal. 

All who libel an associate are^ 
unprofessional, 

This teacher has libelled her Pro- 
associate, J syllogism 
Poly- .'. This teacher is unprofes- 
syllogism \ sional. 

All who are unprofessional YEpi- 

should be disciplined, \ syllogism 

This teacher should be dis- 
ciplined. 



Sorites 251 



4. SORITES. 



A sorites is a series of syllogisms in which all of the 
conclusions are omitted except the last one. 

Just as the epicheirema is a combination of enthymemes 
of the first and second orders, so the sorites is a combina- 
tion of enthymemes of the third order. If each conclu- 
sion were written, the sorites would take the form of 
prosyllogisms and episyllogisms. Two forms of the 
sorites are recognized by logicians. These are the pro- 
gressive or Aristotelian, and the regressive or Goclenian. 
Illustrations. 

Progressive 
Symbolised. Put in Word Form. 

All A is B Thomas Arnold was a teacher, 

All B is C A teacher is a man, 

All C is D A man is a biped, 

All D is E A biped is an animal, 

Hence all A is E Hence Thomas Arnold was an animal. 

Regressive 
All A is B A biped is an animal, 

All C is A A man is a biped, 

All D is C A teacher is a man, 

All E is D Thomas Arnold was a teacher, 

Hence all E is B Hence Thomas Arnold was an animal. 
When regarded from the viewpoint of extension, the 
progressive sorites proceeds from the smaller to the 
larger while the regressive is the converse of this. The 
point may be illustrated by circles : 



252 



Incomplete Syllogisms 




Circle I stands for Thomas Arnold. 
" 2 " " teacher. 

" 3 " man. 

" 4 " " biped. 

" 5 " " animal. 



Fig. 15. 
The progressive sorites proceeds from the smaller circle 
to the larger, thus : 

All of circle I belongs to 2 



2 




•t 


3 


3 


tc 


tt 


4 


4 


tt 


a 


5 


i 


a 


tt 


5 



Hence, " " 

The regressive sorites proceeds from the larger to the 
smaller ; i. e. : 

All of circle 4 belongs to 5 



3 






4 


2 


a 


tt 


3 


1 


a 


a 


2 


1 


tt 


it 


5 



Hence, " " 
Other differences become apparent when the omitted 
conclusions are expressed. 

Progressive 
Symbolized Word Form 

All A is B T. Arnold was a teacher, {A) 

All B is C A teacher is a man, {A) 

.'. All A is C .'. T. Arnold was a man. (A) 
All C is D A man is a biped, (A) 



Sorites 253 

.\ All A is D .'. T. Arnold was a biped. (A) 

All D is E A biped is an animal, (A) 

.'. All A is E .*. T. Arnold was an animal. (A) 

In the three completed syllogisms it becomes evident 
that the progressive sorites uses the minor as its first 
premise and in consequence takes the form of the fourth 
figure, though the reasoning is according to the first figure^ 

The progressive sorites must conform to the following 
rules: 

(1) The first premise may be universal or particular, 
all the others must be universal. 

(2) The last premise may be affirmative or negative; 
all the others must be affirmative. 

A violation of the first rule would result in undis- 
tributed middle; whereas a violation of the second rule 
would give illicit major. These rules may be illustrated 
by giving attention to the symbols of the foregoing 
completed syllogisms. 

The first completed syllogism of the sorites is: 
All A is B 
All B is C 
.*. All A is C 
Securing a logical arrangement by interchanging the 
major and minor premises gives : 

( M ) ( G) ( First premise universal ) 
is C 

(M) 
is B 

(G) 

is C 



(A) 


All B 




(S) 


(A) 


All A 




(S) 


(A) 


.-. All A 



254 Incomplete Syllogisms 

Applying the rules we find this syllogism valid, or we may 

A 
recall that A is valid in the first figure. 
A 
Let us now make the first premise of the sorites par- 
ticular and test. 

Some A is B 
All B is C 
.'. Some A is C 
Arranged logically: 

(M) (G) 
(A) All B is C 





(S) 


(M) 


(I) 


Some A 


is B 




(S) 


(G) 


(I) • 


'. Some A 


is C 



Proof: 

Since one premise is particular the conclusion must be 
particular. (Rule 7) As there are no negatives in the 
argument, only one conclusion is possible; namely, a par- 
ticular affirmative (I). Thus, instead of the conclusion, 
"All A is C," which is an (A), it must be, "Some A is 
C," or an (I). Underscoring the distributed term, it is 
seen that the middle term is distributed in the major 
premise and that no term is distributed in the conclusion. 
Thus the mood is valid. This is "checked" when we 
recall that All is always valid in the first figure. We 
have now shown that the first premise of a progressive 
sorites may be universal or particular. Let us further 



Sorites 255 

proceed to prove that all the other premises must be 
universal. 

Data: Given the first completed syllogism of the sorites: 
All A is B 
All B is C 
.'. All A is C 
Proof: Let any other premise, such as the second, be 
particular; this gives the following: 
All A is B 
Some B is C 
.*. Some A is C 
Arranged logically: Mood, figure, and distribution indi- 
cated. 

(M) (G) 
( I ) Some B is C 
(S) (M) 
(A) All A is B 

(S) (G) 
(I) .'. Some A is C 
We note at once that the middle term is undistributed, 
I 
hence the mood A is invalid in the first figure ; reference 

I 
to the valid moods in figure one "checks" this conclusion. 
Since no premise, other than the first, can be particular, 
then all save the first must be universal. 

The truth of the first rule has been demonstrated, and 
now we may follow a similar plan to prove the truth of 
the second rule. 



256 Incomplete Syllogisms 

Problem: To prove that the last premise may be nega- 
tive.* 
Data : Given the last completed syllogism : 

All A is D 
All D is E 
All A is E 

Let us make the last premise negative (E) and test the 
result. (As all but the first must be universal we cannot 
use an O.) 

All A is D 

No D is E 

.'. No A is E 

Arranged logically and symbolised: 





(M) 


(G) 


(E) 


No D 


is E 




(i) 


(M) 


(A) 


All A 


is D 




(S) 


(G) 


(E) . 


'. No A 


is E 



Proof: Negative premise ; negative conclusion. No par- 
ticulars. Middle term distributed in major premise. No 
term distributed in conclusion which is not distributed in 
premise where it occurs. Syllogism valid. We must now 
prove that all the other premises must be affirmative. 
Problem: To prove that no other premise can be nega- 
tive, or that all others must be affirmative. 
Data: Given last syllogism of sorites with the first 
premise negative. (Any other may be taken.) 

*The student should prove that the last premise may be affirmative. 



Sorites 257 





No A is D 






All D is E 




• 


No A is E 




logically and symbolized: 






(M) 


(G) 


(A) 


All D is 


E 




(S) 


(M) 


(E) 


No A is 


D 




(S) 


(G) 


(E) 


No A is 


E 



Proof: "G" is distributed in the conclusion but not in the 
major premise. Fallacy of illicit major. Hence no other 
premise can be negative. 

We may now consider the completed syllogisms of the 
regressive sorites. 

All A is B 
All C is A 
.*. All C is B 
All D is C 
.*. All D is B 
All E is D 
.'. All E is B 
By examining the foregoing it becomes apparent that 
the regressive sorites, both in form and in the reasoning, 
adapts itself to the first figure. 

The rules of the regressive sorites are just the reverse 
of the progressive. These are : 

( 1 ) The first premise may be negative ; all the others 
must be affirmative. 



258 Incomplete Syllogisms 

(2) The last premise may be particular; all the 
others must be universal. 
It would be a valuable exercise for the student to test 
these rules according to the plan pursued in treating the 
progressive sorites. 

5. IRREGULAR ARGUMENTS. 

It has been intimated that a syllogistic argument, in 
order to be logical, should be made to conform to the 
rules of the syllogism. It must not be inferred from this, 
however, that all deductive reasoning is included by the 
logical forms here treated. There seem to be arguments 
which yield valid conclusions, and yet which are not 
logical in the strict sense of the word. The following 
illustrate some of these forms : 

(1) Quantitative Arguments. 

John is taller than James, 
Albert is taller than John, 
.'. Albert is taller than James. 

Here, apparently, is a fallacy of four terms : these four 
terms are (1) John, (2) taller than James, (3) Albert, 
(4) taller than John. Yet we know that the argument is 
valid. There is not a particle of doubt in the mind rela- 
tive to the truth of the conclusion that "Albert is taller 
than James." We are consequently forced to the infer- 
ence that such quantitative arguments lie outside the field 
of syllogistic reasoning. The argument involves this new 
principle, "Whatever is greater than a second thing which 
is greater than a third thing is itself greater than a third 
thing." 



Irregular Arguments 259 

There are many other arguments similar to this which 
are not syllogistic in nature. To wit: A equals B, B 
equals C, C equals D ; A equals D. A is a brother of B, 
B is a brother of C, C is a brother of D ; A is a brother 
of D. A is west of B, B is west of C, C is west of D; 
A is west of D. 

(2) Plurative Arguments. 

These are arguments in which the propositions are 
introduced by more or most; e. g. : 

Most (more than half) of the team are seniors, 
Most (at least half) of the team are under twenty, 
.'. Some students under twenty are seniors. 
I 
Here we have an I which is evidently valid. No term 

I 
distributed and yet the conclusion is unquestionably true. 
This is due to the fact that the propositions are so worded 
as to force an overlapping of the major and minor terms. 
The student may illustrate this relation by circles. 

6. OUTLINE. 

Incomplete Syllogisms and Irregular Arguments. 

(1) Enthymeme. 

First, second and third orders. 
Natural form. 

(2) Epicheirema. 

Single, double. 

(3) Polysyllogism. 

Prosyllogism, episyllogism. 

(4) Sorites. 

Progressive, regressive. 
Two rules of each. 

(5) Irregular Arguments. 

Quantitative, plurative. 



260 Incomplete Syllogisms 

7. SUMMARY. 

(1) An enthymeme is a syllogism in which one of the three 
propositions is omitted. Suppressing the major premise gives an 
enthymeme of the first order; omitting the minor gives one of 
the second order; while omitting the conclusion gives one of the 
third order. 

The enthymeme is really the natural form of expression. En- 
thymemes of the first order are the most common while those of 
the third order are the most emphatic. 

(2) An epicheirema is a syllogism in which one or more of 
the premises is an enthymeme. An epicheirema is said to \>e 
single when but one premise is an enthymeme, and double when 
both premises are enthymemes. 

(3) A polysyllogism is a series of syllogisms in which the 
conclusion of the preceding syllogism becomes a premise of the 
succeeding one. The one of the series whose conclusion becomes 
a premise is termed a prosyllogism ; while the one which uses the 
conclusion as a premise is called an episyllogism. 

(4) A sorites is a series of syllogisms in which all the conclu- 
sions are omitted except the last one. 

The two kinds of sorites are the progressive and regressive. 
The progressive uses the "minor" as its first premise and adopts 
the form of the fourth figure, whereas the regressive uses the 
"maj or" as its first premise and adopts the form of the first figure, 

The two rules of the progressive sorites are, (1) "The first 
premise may be particular, all the others must be universal"; (2) 
"The last premise may be negative, all the others must be 
affirmative." 

The two rules of the regressive are, (1) "The first premise 
may be negative, all the others must be affirmative"; (2) "The 
last premise may be particular, all the others must be universal". 

(5) Irregular arguments are such as yield valid conclusions 
and yet do not conform to the syllogistic rules. 

The quantitative argument expresses quantity and contains 
four terms. This argument is based on the principle, "What 
ever is greater than a second thing which is greater than a third 
thing is itself greater than a third thing." 

Plurative arguments are introduced by "more" or "most" and 



Summary 26 r 

give in consequence a valid conclusion from two particulars. 
This is due to the overlapping of the major and minor terms. 

8. REVIEW QUESTIONS. 

(1) Define and illustrate an enthymeme. 

(2) Illustrate the enthymemes of the three orders and point 
out their distinct uses. 

(3) Why should the enthymeme demand closer thought than 
the ordinary syllogism ? 

(4) Define and illustrate the epicheirema. 

(5) Of what use is the epicheirema ? Illustrate. 

(6) Define and illustrate a prosyllogism and an episyllogism. 

(7) Why are polysyllogisms so called ? 

(8) Define and illustrate the sorites. 

(9) Relate the sorites and the epicheirema to the enthymeme. 

(10) Illustrate the two forms of sorites. 

(11) Explain the two forms of sorites by means of a diagram. 

(12) Prove the truth of the two rules of the progressive sorites. 

(13) Illustrate two kinds of irregular arguments and show that 
they are valid. 

(14) Complete the five enthymemes of page 248 and indicate 
their mood and figure. 

9. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 

TIGATION. 

(1) Why should enthymemes of the second order be less 
common than those of the first? 

(2) You desire to make it evident to a child that a small 
beginning often leads to a momentous ending; do so in terms of 
the enthymeme of the first order. 

(3) Show that prosyllogism and episyllogism are relative 
terms. 

(4) When the common premise of the "pro" and "epi" 
syllogism is omitted what abbreviated form results? 

(5) From the viewpoint of your definition criticise this : 
"A sorites is a series of prosyllogisms and episyllogisms in which 
all of the conclusions are suppressed except the last." 

(6) Prove the truth of the two rules of the regressive sorites. 



262 Incomplete Syllogisms 

(7) Show that the prosyllogism and the episyllogism may be 
progressive or regressive. 

(8) "Reasoning from cause to effect" — is such progressive 
or regressive ? Explain. 

(9) Which is inductive in nature, the progressive form of rea- 
soning or the regressive? Explain. 

(10) Test the validity of the enthymemes on pages 248 and 
249. 

(11) "A sorites is at least as immediately convincing as the 
chain of syllogisms into which it can be decomposed." Discuss 
this. 



CHAPTER 14. 

CATEGORICAL ARGUMENTS TESTED ACCORDING TO FORM. 

1. ARGUMENTS OF FORM AND MATTER. 

The matter relative to the syllogism treated in chapters 
ii, 12 and 13 is given primarily to enable the reader to 
test the validity of categorical arguments. Such argu- 
ments must be viewed from the two standpoints of form 
and matter, since it is one of the chief purposes of logic 
to enable the student to detect fallacious reasoning, no 
matter how subtly it may be concealed. Therefore, that 
one may gain marked facility in this kind of work, it 
becomes necessary to proceed with thoroughness and 
confidence. The meaning of arguments and the various 
material fallacies may be treated later; but we are now 
equipped with sufficient knowledge and experience to test 
the validity of arguments from the viewpoint of form. 

2. ORDER OF PROCEDURE IN THE FORMAL TESTING 

OF ARGUMENTS. 

In testing categorical arguments three things are essen- 
tial; first, to follow a definite plan; second, to give rea- 
sons; third, to give the author the benefit of the doubt. 
In view of these essentials, we suggest this outline which 
may be helpful to the inexperienced : 

(1) Arrange logically and complete the syllogism. 

(2) Determine the figure and mood by using symbols. 

(3) Apply the rules for negatives and particulars. 



264 Categorical Arguments Tested 

(4) Indicate the distribution by underscoring the 

terms distributed. 

(5) Apply the rules for distribution. 

(6) Name fallacies, if any, giving reasons. 

We recall that to be strictly logical any categorical 
argument must take this form: first, major premise; 
second, minor premise; third, conclusion. Often in com- 
mon conversation either the minor premise or conclusion 
is given first. Illustrations of this: (1) "He cannot be a 
gentleman (conclusion) ; for no gentleman would do such 
a thing (major premise), and there is no doubt but that 
he did it" (minor premise). (2) "He has the making of 
a good teacher (conclusion) ; because he not only knows, 
but he knows how to impart what he knows (minor 
premise), and this is a sure sign of a good teacher" 
(major premise). When the argument appears in this 
illogical form, the first duty of the student is to arrange 
it logically. To do this he must be able to recognize 
readily the premises and the conclusion. To this end 
these facts may be of assistance: 

(1) A premise always answers the question "Why", 

and is often introduced by such words as 
"/or," "because'/ "since;' and the like. 

(2) The conclusion is usually introduced by "there- 

fore;' "hence;' "it follows," etc. 

(3) When there are no word-signs those mentioned 

in the foregoing may be inserted with a view 
of determining which is the conclusion, and 
which are the premises. 



Order of Procedure in Testing of Arguments 265 

Suggestions relative to completing abbreviated argu- 
ments: 

(1) If the conclusion is to be supplied, select the term 
used twice in the premises; this, the middle term, must 
not appear in the conclusion. The other two terms may 
now be connected (copulated) to form the conclusion, 
the narrower term (minor) being used as the subject, 
unless it occurs in what clearly seems to be the major 
premise. (2) If either premise is to be supplied, unite 
the middle term with the subject of the conclusion for the 
minor premise, and with the predicate of the conclusion 
for the major premise. (3) In supplying any missing 
proposition, care should be taken to make the argument 
valid, if this can be done in conformity with good Eng- 
lish, good sense, and the rules of logic. 

As regards the determination of the figure it is well to 
locate the middle term first, placing above it the symbol 
M. Then "G" (greater) may be placed above the major 
term and "S" (smaller) above the minor. 

3. ILLUSTRATIVE EXERCISES IN TESTING ARGUMENTS 
WHICH ARE ALREADY COMPLETE, REGULAR, AND 
LOGICALLY ARRANGED. 

M G 

(1) A All dogs are quadrupeds, 

S M 

A All greyhounds are dogs, 



S G 

All greyhounds are quadrupeds. 



266 Categorical Arguments Tested 

\ A 

This argument is in the first figure, the mood being -J A. 

l A 

All the propositions are affirmative and universal, conse- 
quently the rules pertaining to negatives and particulars 
are inapplicable. "A" distributes the subject only, hence 
all the subjects are underscored. The middle term "dog" 
is distributed in the major premise, and the minor term 
"greyhound" which is distributed in the conclusion, is 
likewise distributed in the minor premise. The argument 
is, therefore, valid in form. This may be verified by 
referring to a list of valid moods in the first figure. 

G M 

(2) E No prejudiced person is open to conviction, 



S M 

All fair minded persons are open to con- 



viction, 

S G 

No fair minded person is prejudiced. 



The argument is in the second figure; mood 



IE 



There is one negative premise and the conclusion is nega- 
tive; no particulars. "E" distributes both terms, "A" the 
subject only. The middle term is distributed in the major 
premise. Both major and minor terms are distributed in 
the conclusion, but they are likewise distributed in the 
premises where they are used. The argument is, there- 



Illustrative Exercises in Testing Arguments 267 

fore, valid. Reference to the valid moods of the second 
figure confirms this conclusion. 

M G 

(3) A All good citizens vote, 

M S 

A All good citizens obey the law, 



S G 

A .*. All who obey the law vote. 

fA 

The mood is -l A used in the third figure. All the prop- 

ositions are A's, hence the negative and particular rules 
are inapplicable. "A" distributes its subject. The middle 
term is distributed in both premises. "All who obey 
the law" is distributed in the conclusion but not in the 
premise where it is used. Therefore the argument is 

fA 
invalid. The fallacy being illicit minor. ■ 



in the third figure's list of valid moods. 
M G 

(4) A All good citizens vote, 



A is not found 
A 



S M 

E No criminal is a good citizen, 



S G 

E .*. No criminal votes. 



. (A 

The mood of this argument is -{E used in the first 



268 Categorical Arguments Tested 

figure. One premise negative; conclusion negative; no 
particulars. "A" distributes the subject only; "E" both 
subject and predicate. The middle term, "good citizens," 
is distributed in both premises. The major term, "votes," 
is distributed in the conclusion but not in the premise 
where it is used. The argument is invalid, the fallacy 
(A 

E is not found in the first figure's 

E 



being illicit major. 
list of valid moods. 



G M 

(5) A All true teachers are sympathetic, 



S M 

A All lovers of children are sympathetic, 



S G 

A .*. All lovers of children are true teachers. 



The mood of this argument is 



(A 

A used in the second 

A 

figure. There are no negatives and no particulars. "A" 
distributes its subject only. The middle term, "sympa- 
thetic," is distributed in neither premise, hence the argu- 
ment is invalid. Fallacy of undistributed middle. Re- 

' A 
ferring to the list of valid moods, we do not find -| A in 

the second figure. 

M G 

(6) A All thoughtful men are humane, 



Illustrative Exercises in Testing Arguments 269 

S M 

A All good citizens are thoughtful men, 



S G 

I .'. Some good citizens are humane. 

r A 
The mood is J A in the first figure. No negatives ; no 
I 
particulars. "A" distributes its subject only; "I" dis- 
tributes neither term. Middle term, distributed in the 
major premise; no term distributed in the conclusion. 
The argument is, therefore, valid. The conclusion is 
weakened as it could just as well be an A. The mood 
A 

A in the first figure is valid, but of little value because 
I 
of the weakened conclusion. 

4. ILLUSTRATIVE EXERCISE IN TESTING COMPLETED 
ARGUMENTS, ONE OR BOTH PREMISES BEING IL- 
LOGICAL. 

Arguments containing exclusive propositions. 
( 1 ) Only first class passengers may ride in the parlor 
car, 
All these are first class passengers, 
.'. They may ride in the parlor car. 
Propositions introduced by such words as only, none 
but, alone and their equivalents are exclusive proposi- 
tions. Since these distribute their predicates, but do not 
distribute their subjects, the most convenient way of deal- 
ing with them is to interchange subject and predicate and 



270 Categorical Arguments Tested 

then regard them as "A" propositions. As the first prop- 
osition of the argument is an exclusive, we must deal with 
it accordingly. Interchanging subject and predicate and 
introducing it with all places the argument in this form: 
G M 

A (All) The parlor car is reserved for first class 



passengers, 
S M 

A All these are first class passengers, 

~~S~ G 

A .'. All these may ride in the parlor car. 



XA 

The mood of this argument is^j A in the second figure . 

l A 

No negatives; no particulars. "A" distributes its sub- 
ject only; the middle term is thus undistributed. The 
argument is invalid, the fallacy being that of undistributed 
middle. 

(2) "No one but a thief would take these books with- 
out asking for them, and it has been proved that you took 
the books; that is the reason I have called you a thief." 

It is clear that "no one but" is equivalent to "only." 
Thus the first proposition of the argument is an ex- 
clusive, and may be made logical by interchanging subject 
and predicate and calling it an "A." As a result of this 
the argument takes the following form: 

M G 

A (All) These books were taken by a thief, 



Exercise in Testing Completed Arguments 271 

S M 

You took these books, 



S G 

A .'. You are a thief. 



We have now had sufficient experience to recognize 
the validity of mood AAA in the first figure. 

(3) "None but the brave deserve the fair, 

And you are not fair." 
Making the exclusive logical and completing gives : 
M G 

A (All) The fair deserve the brave, 



S M 

You are not fair, 



S G 

. You do not deserve the brave. 



The mood of this argument is<J E used in the first fig- 

ure. There is a negative premise, also a negative con- 
clusion; no particulars. The middle term is distributed 
twice. The major term "brave" is distributed in the con- 
clusion but not in the major premise ; hence the argument 
is invalid, the fallacy being illicit major. 

Note. — There may be some doubt in the student's 
mind as to the proposition "None but the brave deserve 
the fair," really meaning "All the fair deserve the brave." 



2.J2. Categorical Arguments Tested 

This doubt may be better satisfied by treating the ex- 
clusive in the second way as indicated on page 137, 
to wit: Negate the subject of the exclusive, then give it 
the form of the regular "E." This results in "No not- 
brave persons deserve the fair," which, after first convert- 
ing and then obverting becomes, "All the fair deserve the 
brave." 

Arguments Containing Individual Propositions. 

(4) "George Washington never told a lie, but you, 
when tempted, yielded with no qualms of conscience." 

Completing, and arranging logically gives: 
E George Washington never told a lie, 



You did tell a lie, 



E .'. You (in this respect) are not like George 



Washington. 

Treated properly this argument proves to be valid; the 
student, however, is apt to deal with such in this wise : 
O George Washington never told a lie, 

I You did tell a lie, 



O .*. You (in this respect) are not like George 



Washington. 

When placed in this mood the argument is invalid ; since 
the major term, which is distributed in the conclusion, 
is not distributed in the premise where it occurs (illicit 
major). It is the tendency on the part of students to 
classify as particular, a proposition which has as its sub- 



Exercise in Testing Completed Arguments 273 

ject a singular term. Such propositions we have learned 
to call individual. The cause of this tendency is easily 
explained: Consider the propositions, (1) "This man is 
mortal"; (2) "Some men are mortal"; (3) "All men are 
mortal." In the first instance "mortal" refers to the sub- 
ject "man" which is narrower in significance than "some 
men" to which "mortal" of the second proposition refers. 
In consequence, it is very natural to infer that if, "Some 
men are mortal" is particular, then, "This man is mortal" 
is likewise particular. The error springs from a wrong 
conception of particular as used in logic; the content of 
the term has little to do with extension, but is chiefly 
concerned with indefiniteness. A particular proposition 
is one in which the predicate refers to only a part of an 
indefinite subject. If the subject is referred to as a 
whole, and this whole is more or less definite, then the 
proposition is universal. Since "mortal" refers to the 
whole of the definite term "this man" as positively as it 
refers to the whole of "all men" there is as much justifi- 
cation in calling the first proposition universal as there 
is in calling the third universal. It may be remembered, 
then, that logicians class as universal all individual 
propositions. 

Arguments Containing Partitive Propositions. 

(5) All that glitters is not gold, 
Tinsel glitters, 
.'. Tinsel is not gold. 

The quantity sign "all" when used with "not" is am- 
biguous ; it may mean "no" or "some-not. ,} The only way 
to determine which meaning is intended is to try both 



274 Categorical Arguments Tested 

these quantity signs, selecting the one which seems to 
fit best the author's meaning. When "ail-not" means 
"some-not" the proposition which it introduces is called a 
partitive proposition; since such always suggests a com- 
plementary proposition. (See page 133.) For ex- 
ample, "Some glittering things are not gold/' suggests 
its complement, "Some glittering things are gold." In 
testing the foregoing argument it is clear that "All that 
glitters is not gold" does not mean "No glittering thing 
is gold/' so much as it implies "Some glittering things 
are not gold." Thus the argument takes this form: 
M G 

O Some glittering things are not gold, 

S M 

A Tinsel glitters, 



S G 

Tinsel is not gold. 



The mood is«{ A in the first figure. There is one negative 

premise (O), and the conclusion is negative. There is 
one particular premise (O), but the conclusion is not 
particular. This makes the argument invalid according 
to rule 8; viz.: "A particular premise necessitates a 
particular conclusion." Carrying the test still further it 
will be seen that there is likewise the fallacy of undis- 
tributed middle. 

Other arguments where one of the premises is partitive. 

"All scholars are not wise and, therefore, Aristotle 



Exercise in Testing Completed Arguments 275 

was not wise." "All democrats are not free-traders, but 
most of the men of this particular club are democrats, 
and hence they are of a different faith (not free-traders). 

"All the members of the club are not good players, 
and James belongs to the club." 

"All educated men do not write good English; there- 
fore, you ought not to express surprise when informed 
that X, though an educated man, uses poor English." 

The major premise in each of the foregoing is partitive 
in nature and should be changed to the following form 
before the argument is tested; taking these in order we 
have: "Some scholars are not wise"; "Some democrats 
are not free-traders" ; "Some of the members of the club 
are not good players" ; "Some educated men do not write 
good English." Let us test the validity of the last one: 

(6) O Some educated men do not write good 



English, 
A X is an educated man 



E .". X does not write good English (uses poor 



English, 
Like the first one of the list, this is invalid inasmuch as a 
particular premise should yield a particular conclusion, 
not one which is universal. The argument also contains 
the fallacy of undistributed middle. 

Arguments Containing Inverted Propositions. 

(7) "Blessed are the merciful: for they shall obtain 
mercy." The first proposition, being poetical in con- 



276 Categorical Arguments Tested 

struction, is typical of the inverted form. These are 
usually made logical by simple conversion. Since prem- 
ises usually follow "for," or equivalent word-signs, it is 
easy to see that "for they shall obtain mercy" is one of 
the premises ; while the other, the broader of the two, is 
understood. 

Arranged logically the argument assumes this form : 

M G 

A Those who obtain mercy are blessed, 



S M 

The merciful shall obtain mercy, 



S, G 

The merciful are blessed. 



Here we have the mood-j A in the first figure, which we 

l A 

know to be valid. 

Other agruments where one of the propositions is 
inverted. 

"Blessed are the pure in heart : for they shall see God." 

"To thine own self be true, and it must follow, as the 
night the day, thou canst not then be false to any man." 

"A king thou art and, therefore, thy commands shall 
be, yea, must be obeyed." 

Taking the inverted propositions in order and making 
each logical, the following is the result: "The pure in 
heart are blessed" ; "You be true to yourself, and . . " ; 
"You are a king, therefore . . ." 



Arguments which are Incomplete 277 

5. ARGUMENTS WHICH ARE INCOMPLETE AND MORE 
OR LESS IRREGULAR. 

(1) "He must be a star player; for he played full- 
back on the team which won the championship." 

(2) "The man is not to be trusted; because he served 
a term of 90 days in jail." 

(3) "Only material bodies gravitate, and ether does 
not gravitate." 

(4) "If only fools despise knowledge, this man cannot 
be a fool." 

(5) "A charitable man has no merit in relieving dis- 
tress ; because he merely does what is pleasing to himself." 

(6) "It is evident that all who get justice buy it; 
since only the rich get it." 

The above arguments thrown into logical form and 
validity or invalidity stated: (The student should test 
these in detail.) 

M 
(1) A All belonging to the team which won the 



G 

championship were star players, 



S M 

He played with the team which won the 

championship, 

S G 

He is a star player. Valid in form. 



278 Categorical Arguments Tested 

M 

(2) E One who serves a term of 90 days in jail 

' G 

is not to be trusted, 



S M 

This man served a term of 90 days in jail, 



S G 

This man is not to be trusted. Valid in 



form. 



M G 

(3) A All gravitating bodies are material, 



S M 

E Ether does not gravitate, 



S G 

E .'. Ether is not material. Illicit major. 



M G 

(4) A All who despise knowledge are fools, 



S M 

E This man does not despise knowledge, 



S G 

E .'. This man is not a fool. Illicit major. 



M 
(5) E No one who merely does what is pleasing 



Arguments zvhich are Incomplete 279 

G 

to himself has merit in relieving distress, 



S 
A A charitable man merely does what is 



M 

pleasing to himself, 

S G 

E .'. No charitable man has merit in relieving 



distress. Valid in form. 



M G 

(6) A All the rich buy justice, 



S M 

A All who get justice are rich, 



S G 

A .*. All who get justice buy it. Valid in form. 



In supplying suppressed premises the critic is duty 
bound to give the author the benefit of the doubt, if by 
so doing no principle in logic is violated and the propo- 
sition conforms to good English and good sense. Often 
it is not easy to perceive in the abbreviated argument the 
meaning intended; in such instances all legitimate effort 
should be directed to making the argument valid. To 
illustrate: In supplying the major premise of argument 
"6" it would be easy to make it, "All justice is bought 
by the rich" ; in consequence the critic could pronounce 



280 Categorical Arguments Tested 

the argument invalid as the middle term would be undis- 
tributed. 

Before asserting that an argument is fallacious because 
it has four terms rather than three, the student must make 
sure that there are no synonyms or equivalents used. In 
argument "4," for instance, there are apparently the four 
terms: (1) "foolish," (2) "despise knowledge," (3) 
"man," (4) "fool" ; but to regard "foolish" and "fool" as 
synonyms does not seem like undue liberty. The follow- 
ing arguments further illustrate this need of recognizing 
synonyms: 

"Human beings are accountable for their conduct; 
brutes, not being human, are therefore free from re- 
sponsibility." (Not accountable for their conduct.) 

"Not all educated men spell correctly; because one 
often finds mistakes in the writings of college graduates." 
(Educated men.) 

"Modern education is not popular in this state; for it 
increases the tax rate, and the popularity of everything, 
which touches the pocket of these frugal Yankees, (in- 
creases the tax rate) is very short lived." (Not popular.) 
In common parlance the use of synonyms is so prevalent 
that ready ability to substitute equivalents in word, phrase, 
and clause form is needed by him who would be skillful 
in testing all kinds of arguments. 

It has already become apparent to the student that the 
number of the noun or the tense of the verb is of small 
logical consequence. A very large proportion of the 
formal fallacies in argumentation concern the rules 



Arguments which are Incomplete 281 

of distribution which are summarized in the dictum 
"What may be said of the whole may be said of part of 
that whole." 

6. COMMON MISTAKES OF STUDENTS IN TESTING 

ARGUMENTS. 

The most common mistakes made by the student when 
testing arguments are as follows : ( 1 ) Using the exclusive 
as an "A" without interchanging subject and predicate; e.g., 
interpreting the proposition, "Only high school graduates 
may enter the training school," as meaning "All high 
school graduates may enter the training school." (2) 
Calling individual propositions particular; e. g., interpret- 
ing "Socrates is mortal" as an "I" rather than an "A." 
(3) Signifying that partitive propositions are "A's" 
rather than "O's"; e. g., "All that glitters is not gold" 
interpreted as meaning that "All glittering things are 
gold," rather than "Some glittering things are not gold." 
(A). (4) Concluding that a fallacy of four terms has 
been committed when two terms are synonomous. (5) 
Failing to interchange the subject and predicate of 
inverted propositions. 

7. OUTLINE. 

Categorical Arguments Tested According to Form. 

(1) Arguments of form and matter. 

(2) Order of procedure in the formal testing of arguments. 

The outline. 

Determining premises and conclusion. 

Completing abbreviated arguments. 



282 Categorical Arguments Tested 

(3) Illustrative exercises in testing arguments which are com- 
plete and whose premises are logical. 

(4) Illustrative exercises in testing completed arguments, one 
or both of whose premises are illogical. 

Exclusive premises, individual premises, partitive 
premises, inverted premises. 

(5) Incomplete and irregular arguments. 

(6) Common mistakes of the student. 

8. SUMMARY. 

(1) In determining their validity, arguments must be tested 
from the two viewpoints of form and matter. 

(2) In testing categorical arguments it is quite necessary to be 
definite, to give reasons, and to give the author the benefit of the 
doubt. 

With this in view the attending outline is suggestive : 

1. Arrange logically and complete. 

2. Determine the figure and mood. 

3. Apply rules for negatives and particulars. 

4. Indicate distribution. 

5. Apply rules for distribution. 

6. Name fallacies, if any, giving reasons. 
The logical arrangement of syllogistic arguments is 

1. Major premise. 

2. Minor premise. 

3. Conclusion. 

Any proposition in a syllogism which answers the question 
"Why?" is a premise, whereas the conclusion follows "therefore", 
or its equivalent either written or understood. If a conclusion is 
to be supplied, unite the two terms which are used but once in 
the premises, using the "minor premise term" as the subject. If 
a premise is to be supplied, unite the middle term with the 
"minor" to form the minor premise and with the "major" to 
form the major premise. 

(3) Arguments which are regular, complete, and logically ar- 
ranged, may be tested by symbolizing the mood and figure, under- 
scoring the distributed terms, and then applying the general rules 
of the syllogism. 

(4) Arguments with illogical premises may not be tested with 



Summary 283 

impunity till the faulty premises are made logical. The exclusive, 
an illogical proposition introduced by only, alone, none but, and 
the like, may be made logical by interchanging subject and predi- 
cate and calling the proposition an A. The individual proposition 
is one with a singular subject. In testing, individual propositions 
are classed as universal. Propositions introduced by "all-not"are 
usually given the significance of"some-not". These are called 
partitive propositions, which in the testing, should be denominated 
"O's". 

Inverted propositions when subjected to the test for va- 
lidity must be converted simply and then classified. (Usually as 
A's.) 

(5) In supplying propositions which are taken for granted, the 
aim should be to make the argument valid, provided this can be 
done without violating the rules of logic, English, and common 
sense. 

Ability to substitute equivalent words, phrases, or clauses is de- 
manded of the student of logic, inasmuch as such substitution is 
frequently needed in the testing of arguments. 

Number and tense have little significance in dealing with argu- 
ments. 

(6) The common mistakes of students made in testing argu- 
ments concern exclusive, partitive and inverted propositions, and 
an inability to recognize expressions equivalent in meaning. 

9. REVIEW QUESTIONS. 

(1) Name and explain the two standpoints from which all 
arguments must be viewed. 

(2) Give an outline of procedure which may be serviceable in 
the testing of categorical arguments. 

(3) Give illustrations showing that the logical order of cate- 
gorical arguments is not the usual mode of procedure in common 
parlance. 

(4) Offer suggestions which may aid in designating a premise ; 
a conclusion. 

(5) How would you proceed in forming any one of the three 
propositions of a syllogism when the other two are given ? 



284 Categorical Arguments Tested 

(6) Designate the premises and the conclusion in the follow- 
ing, supplying any proposition which may be omitted, also 
arrange logically and test the validity. 

(1) "The people of this country are suffering from an 

overdose of prosperity; consequently a period of 
hard times will be a valuable lesson." (The conclu- 
sion should be recast so as to read, "A period of 
hard times will cure the people of this country." 
The minor premise is, "Those who suffer from an 
overdose of prosperity may be cured by a period of 
hard times") 

(2) "I am a teacher; you are not what I am; hence you 
are not a teacher." 

(3) "To kill a man is murder, therefore war is murder." 

(4) You have not adopted the best policy since honesty 

has always been and will always be the best policy." 

(5) "Since the road is criminally mismanaged, why should 

not the authorities be indicted as criminals ?" 

(6) "Early to bed and early to rise makes a man healthy, 

wealthy and wise. I am none of these; hence my 
sleeping hours have been wrong." 

(7) Illustrate a weakened conclusion. 

(8) Explain the exclusive proposition and indicate how the 
logician should treat it. 

(9) Arrange logically and test the following: 

(1) Only weak men become intemperate, and Edgar 
Allen Poe was surely intemperate. 

(2) No admittance except on business; hence you can- 

not be admitted. 

(3) Virtuous acts are praiseworthy, and indiscrim- 

inate giving is not a virtuous act. 

(10) Explain why individual propositions are classed as uni- 
versal. 

(11) Write an argument whose major premise is a partitive 
proposition; arrange logically and test validity. 

(12) Arrange and test this argument: "Blessed are the poor in 
spirit: for theirs is the kingdom of heaven." 



Review Questions 285 

(13) Complete, arrange and test. 

(1) "The object of war is to settle disputes; hence 
soldiers are the best peacemakers." 

(2) "The various species of brutes being created to prey 
upon one another proves that man is intended to 
prey upon them." 

(3) "The end of everything is its perfection; death being 
the end of life is its perfection." 

(4) "All the trees of the yard make a thick shade and 
this is one of them." 

(5) '"Minds of moderate caliber ordinarily condemn 

everything which is beyond their range, and his is 
such a mind." 

(6) "The best of all medicines are fresh air and sleep, 
and you are sorely in need of both." 

(7) "Every hen comes from an egg; every egg comes 

from a hen; therefore every egg comes from an 
egg." 

(8) "He cannot have been there — otherwise I should 
have seen him." 

(14) "It is fair to give the author the benefit of the doubt when 
we set ourselves up as censors worthy of the name." Explain 
this. 

(15) Illustrate by citing arguments the need of detecting terms 
which are equivalents in signification. 

(16) How does the logician look upon number and tense as 
treated in grammar ? 

(17) Illustrate and test an argument in which one of the pre- 
mises is elliptical. 

(18) Summarize the most common mistakes made by students 
in the testing of categorical arguments; illustrate these mistakes 
and then write in logical form. 

10. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Give illustrations of arguments which are valid in form 
but invalid in meaning. Explain. 



286 Categorical Arguments Tested 

(2) May an argument be valid in meaning but invalid in 
form ? Exemplify. 

(3) Put a simple problem in arithmetic in syllogistic form and 
show that the minor premise naturally comes first. 

(4) In the practice of law is there any custom analagous to 
giving the author the benefit of the doubt in logical argumenta- 
tion ? 

(5) Test in detail the following arguments: 

(1) "All wise presidents strive to give heed to the de- 
mands of the people, but this president has not done 
so." 

(2) "The existence of God is not universally believed, 
hence it cannot be true." 

(3) "The institution has prospered under the present 

regime therefore why change it?" 
"The man is guilty because seven out of the nine 
witnesses so testified." 
(5) "I know three men who cleared not less than ten 
thousand dollars in this business; and why cannot 
I do as much?" 

(6) "Only members may vote and, since you are not a mem- 
ber, you will not be allowed to vote." Change the exclusive in 
this argument in the two ways suggested in Chapter 8, page 
126. Test the argument in both cases. 

(7) Show by illustration that the quantity sign "all" when 
used with "nof may in some cases mean "no" and in others 
" some-no f. 

(8) Make two selections from some poet of authority rep- 
resenting arguments with an inverted premise. 

(9) Select from news papers three arguments which seem to 
illustrate the fallacy of four terms but which in reality do not. 
Explain. 

(10) Wherein could the elliptical proposition lead to error? 

(11) Put the following in syllogistic form and test: 

(1) "That persons may reason without language is 
proven by the circumstances that infants reason 
and yet have no language." 



Review Questions 287 

(2) "The scriptures cannot come from God because they 

contain some things which cannot be comprehended 
by man." 

(3) "When Columbus was sailing the ocean in search 

of a new world, Ik fell in with a flock of land birds 
and concluded that he could not be far from land." 

(4) "Bolingbroke in arguing against the truth of the 

Christian religion shows that the Christian religion 

has bred contentions." "Burke answered him by 

showing that civil government had bred conten- 
tions." 



CHAPTER 15. 

HYPOTHETICAL ARGUMENTS, AND DISJUNCTIVE ARGUMENTS 
INCLUDING THE DILEMMA. 

1. THREE KINDS OF ARGUMENTS. 

The proposition, constituting the basic unit of the argu- 
ment, would of necessity be indicative of the nature of 
said argument ; therefore the three general kinds of prop- 
ositions, categorical, hypothetical and disjunctive, suggest 
the three kinds of arguments which are in turn cate- 
gorical, hypothetical and disjunctive. Categorical argu- 
ments are those in which all of the propositions are cate- 
gorical. Since this kind has been treated, it remains for 
us to consider the other two. 

2. HYPOTHETICAL ARGUMENTS. 

We have observed that a hypothetical proposition is 
one in which the assertion depends on a condition; for 
example, in the proposition, "If it is pleasant, I will call 
on you to-morrow," the calling depends on the state of 
the weather. "I will call on you to-morrow," is the 
assertion which is limited by the condition, "If the 
weather is pleasant." Definition : 

The hypothetical argument or syllogism is one in which 
the major premise is hypothetical and the minor premise 
categorical. 

288 



Hypothetical Arguments 289 

Illustration : 

If the people are right more than half of the time, the 
world will progress ; 

And the people are right more than half of the time, 

Hence the world will progress. 

In contradistinction to disjunctives, hypothetical propo- 
sitions and hypothetical syllogisms are frequently re- 
ferred to as "conjunctive." 

3. THE ANTECEDENT AND CONSEQUENT. 

Facility in detecting the antecedent and consequent of 
hypotheticals is required in order to deal intelligently 
with the argument. The hypothetical proposition has 
been defined as one in which the assertion is limited by a 
condition. The consequent is the assertion and usually 
follows (though not always) the antecedent which is the 
limiting condition. First the antecedent and then the 
consequent is the logical order as the derivative meaning 
of the words antecedent and consequent would indicate. 
The antecedent is introduced by such words as "if," 
"though," "unless," "suppose," "granted that," "when," 
etc. 

Illustrations : 

Antecedent. Consequent. 

1. If you study, you will pass. 

2. If it rains, it is cloudy. 

3. If two is added to three, the result is five. 

4. If you are temperate, you will live to a ripe old 

age. 



290 Hypothetical and Disjunctive Arguments 

Consequent. Antecedent. 

5. I will go, unless you wire me to the 

contrary. 

6. I will pay you, when you present your bill. 

7. I shall make the trip in granted that I have no acci- 
ten hours, dents. 

8. My overcoat would not 

have been stolen, if the door had been locked. 

4. TWO KINDS OF HYPOTHETICAL ARGUMENTS. 

The two kinds of hypothetical syllogisms are the con- 
structive and destructive. 

A constructive hypothetical syllogism is one in which 
the minor premise affirms the antecedent. 

A destructive hypothetical syllogism is one in which the 
minor premise denies the consequent. 

The constructive hypothetical is sometimes referred to 
as the "modus ponens" ; whereas the destructive hypo- 
thetical is called the (f modus tollens." 
Illustrations : 

Constructive Hypothetical Syllogisms. 
Symbols. Words. 

If A is B, C is D If you are diligent, you will suc- 
ceed; 
A is B And you are diligent, 

.\ C is D Therefore you will succeed. 

Destructive Hypothetical Syllogisms. 
If A is B, C is D If you had been diligent, you would 
have succeeded; 
C is not D But you did not succeed, 

.*. A is not B Therefore you were not diligent. 



Rule and Fallacies of the Hypothetical 291 

5. THE RULE AND TWO FALLACIES OF THE HYPO- 
THETICAL ARGUMENT. 

From a given hypothetical proposition it is possible to 
construct four different hypothetical syllogisms, as the 
attending illustrations make evident: 

Consider the hypothetical proposition "If it has rained, 
the ground is damp." 

(1) Minor premise affirms antecedent. 

If it has rained, the ground is damp; 

It has rained, 

Therefore the ground is damp. 

(2) Minor premise denies antecedent. 

If it has rained, the ground is damp; 

It has not rained, 

Therefore the ground is not damp. 

(3) Minor premise affirms consequent. 

If it has rained, the ground is damp ; 
The ground is damp, 
Therefore it has rained. 

(4) Minor premise denies the consequent. 

If it has rained, the ground is damp ; 

The ground is not damp, 

Therefore it has not rained. 
Without any knowledge of the rules of the hypothetical 
syllogism let us strive to determine how many of the 
foregoing are valid. Relative to the first, it would be 
impossible for any rain to fall without making the ground 
somewhat damp; a few drops would be sufficient. In 
short, if the antecedent happens, the consequent must 
follow. It seems, therefore, that the first argument is 



292 Hypothetical and Disjunctive Arguments 

valid. Considering the second : rain is not the only cause 
for the dampness of the ground, as it might result from 
the falling of dew, or from a dense fog; no rain does not 
necessarily mean no dampness. It is clear that if the ante- 
cedent does not happen, the consequent may or may not 
follow. Thus it appears that the second argument is 
invalid. Attention to the third makes evident a condition 
similar to the second : the ground may be made damp by 
agencies other than rain, such as fog and dew. Thus the 
third argument is likewise mvalid. But in the fourth 
argument it is obvious that if the ground is not damp, 
then there could have been. neither rain, nor fog, nor dew. 
No dampness shuts out all of the conditions, including the 
rain. Therefore the fourth argument is valid. 

This investigation suggests a rule for hypothetical argu- 
ments. Since only the first and fourth arguments are 
valid, this is the rule which must obtain: The minor 
premise should either affirm the antecedent or deny the 
consequent. 

Any violation of this rule would result in the fallacies 
of denying the antecedent or affirming the consequent. 

There is one exception to this rule which must not be 
overlooked; viz.: If the antecedent and consequent of 
the hypothetical proposition are co-extensive then both 
may be either affirmed or denied. 

Illustrations : 

(1) If the rectangle is equilateral, then it is a square; 

The rectangle is equilateral, 
.'. It is a square. 



Rule and Fallacies of the Hypothetical 293 

(2) If the rectangle is equilateral, then it is a square; 
The rectangle is not equilateral, 

.*. The rectangle is not a square. 

(3) If the rectangle is equilateral, then it is a square; 
It is a square, 

.'. The rectangle is equilateral. 

(4) If the rectangle is equilateral, then it is a square ; 
It is not a square, 

.'. The rectangle is not equilateral. 

6. HYPOTHETICAL ARGUMENTS REDUCED TO THE 
CATEGORICAL FORM. 

The hypothetical syllogism so closely resembles the 
categorical that it may be changed to it by a slight altera- 
tion in the wording. After testing the hypothetical by its 
own rule, it may be expedient to reduce the argument to 
the categorical form, and subject it to a second test in 
which the categorical rules are applied. This reduction 
usually necessitates two steps; first, change the proposi- 
tions which represent the antecedent and consequent to a 
subject term and a predicate term respectively and then 
unite them to form the major premise; second, supply a 
new minor term, if necessary. 

Illustrations of Reduction; and Comparison of Hypo- 
thetical and Categorical Fallacies: 

Hypothetical Form: 

(1) If it has rained, the ground is damp; 
It has rained, 
.'. The ground is damp. 



294 Hypothetical and Disjunctive Arguments 

Categorical Form: 

M G 

A The falling rain makes the ground damp, 



S M 

In this case rain has fallen, 



S G 

A .'. In this case the ground is damp ground. 



It is seen that the argument in the hypothetical form 
is valid as the minor premise affirms the antecedent. 
Reducing to the categorical gives to the argument the 

mode \K in the first figure which we know to be valid. 
IA 

Hypothetical: 

(2) If one were wise, he would study; 
But you will not study, 
.'. You are not wise. 

Categorical: 

G M 

A A wise person would study, 



S M 

E You will not study, 



S G 

. You are not wise. 



In the hypothetical form the argument is valid since 
the minor premise denies the consequent. Reducing to 



Hypothetical Arguments Reduced 295 

A 

the categorical gives mood E in the second figure. This 

E 
is valid. 

Hypothetical: 

(3) If the wind blows from the south, it will rain; 
But the wind is not blowing from the south, 
Hence it is not going to rain. 

Categorical: 

M G 

A South wind brings rain, 



S M 

E This wind is not a south wind, 



S G 

This wind will not bring rain. 



Hypothetically considered, the minor premise denies 
the antecedent and consequently the argument is invalid. 
Reducing to the categorical form, it is found that the 
major term is distributed in the conclusion, but is not 
distributed in the major premise; hence the fallacy of 
illicit major is committed. 

Hypothetical: 

(4) If a man is just, he will obey the golden rule; 
This judge has obeyed the golden rule, 
Hence he is just. 



296 Hypothetical and Disjunctive Arguments 

Categorical: 

G M 

A A just man will obey the golden rule, 



S M 

A This judge has obeyed the golden rule, 



S G 

A .'. This judge is a just man. 



Hypothetically considered, the minor premise affirms 
the consequent and thus the argument is fallacious; 
when changed to the categorical we find the fallacy of 
undistributed middle. If other examples were taken, it 
could be proved that the hypothetical fallacy of denying 
the antecedent is usually equivalent to the categorical 
fallacy of illicit major; whereas the hypothetical fallacy 
of affirming the consequent amounts to undistributed 
middle. 

In reducing some hypothetical it is necessary to make 
use of such expressions as, "the case of or "the circum- 
stances that." The attending argument will illustrate 
this: 

If Jefferson was right, man was created free 
and equal; 

(but) Man was not created free and equal, 
.'. Jefferson was not right. 

Reduced to the categorical: 

G 
The case of Jefferson being right is the case of man 



Hypothetical Arguments Reduced 297 

M 
being created free and equal ; 
S M 

Man was not created free and equal, 



S G 

.'. Jefferson (this man) was not right. 



The argument is valid in both cases. 

7. ILLUSTRATIVE EXERCISE TESTING HYPOTHETICAL 
ARGUMENTS OF ALL KINDS. 

The following brief outline may be followed in testing 
hypothetical arguments : 

1. Arrange logically. 

2. Determine antecedent and consequent. 

3. Apply the hypothetical rule ; name fallacies giving 

reasons. 

4. Reduce to categorical form. 

5. Apply the categorical rules, giving fallacies with 

reasons. 

(1) If a man is properly educated, he will not despise 

manual labor; 
therefore I conclude that you have not been 

properly educated, 
since you dislike to work with your hands. 

Arranged logically and antecedent and consequent indi- 
cated: 

If a man is properly educated (antecedent), he will 
not despise manual labor (consequent) ; 



298 Hypothetical and Disjunctive Arguments 

You despise manual labor (dislike to work with your 
hands), 
.'. You have not been properly educated. 
The minor premise denies the consequent, hence the argu- 
ment is valid according to the rule, "The minor premise 
must affirm the antecedent or deny the consequent." The 
student should note that the consequent is negative and 
therefore its denial must be an affirmative proposition. 
Reduced to the categorical: 
G 
E A properly educated man will not despise 





M 




manual labor; 




S M 


A 


You despise manual labor, 




S G 


E . 


'. You have not been properly educated. 



Regarded categorically this is valid. Why? 

(2) "If one believes in the tenets of the democratic 
party, then he should vote for its candidates ; and since A 
does believe in them I have asked him to vote for me." 
Arranged, and antecedent and consequent indicated. 
If one believes in the tenets of the democratic party 
(antecedent), then he should vote for its candi- 
dates (consequent) ; 
And A does believe in these tenets, 
.'. He should vote for its candidates (I have asked him 
to vote for me). 



Illustrative Exercises 299 

The minor premise affirms the antecedent and thus the 
argument is valid according to rule. 
Reduced to the categorical: 

M 
A One who believes in the tenets of the demo- 

G 

cratic party should vote for its candidates, 



S M 

A A believes in these tenets, 

S~ G 

A .'. A should vote for its candidates. 

f A 

Reduced to the categorical gives mood < A in the first 

I a 

figure and this we know to be valid. 

(3) "If the weather had not been pleasant, I could not 
have come ; but as the weather is pleasant, here I am." 
Arranged and antecedent and consequent indicated: 
If the weather had not been pleasant (antecedent), I 

could not have come (consequent) ; 
The weather is pleasant, 
.'. I have come (here I am). 

The minor premise denies the antecedent and conse- 
quently the argument is invalid according to the rule. 
(An affirmative minor premise denies a negative ante- 
cedent.) 

Reduced to the categorical: 

E Unpleasant weather would not permit me to 
come, 



300 Hypothetical and Disjunctive Arguments 

E This weather is not unpleasant, 
A .'. This weather enabled me to come. 
Fallacy of two negative premises. 
(4) "If one pays his debts, he will not be 'black-listed' ; 
but since you are 'black-listed,' I conclude that you have 
not paid your debts." 

Arranged logically and antecedent and consequent indi- 
cated: 

If one pays his debts (antecedent), he will not be 

"black-listed" (consequent) ; 
You are "black-listed," 
.'. You have not paid your debts. 

The minor premise denies the consequent hence the argu- 
ment is valid. 

Reduced to categorical form: 

G M 

E No one who pays his debts is black listed, 



S M 

You are black listed, 

in g 

You have not paid your debts. 



[ E . 

The mood \ A in the second figure is valid. 
IE 
(5) "Men would do right for the sake of themselves, 
if they appreciated the law of retribution ; but they never 
think of that." 

Arranged, completed, and tested: 
If they appreciated the law of retribution (ante- 



Illustrative Exercises 301 

cedent), men would do right for the sake of them- 
selves (consequent) ; 
But they do not appreciate the law of retribution 
(never think of that), 

Hence they do not do right for the sake of themselves. 
Fallacy of denying the antecedent. 
Reduced to the categorical: 

M 
A The case of men appreciating the law of retri- 



G 
bution, is the case of men doing right for 



the sake of themselves ; 
S M 

But men do not appreciate the law of retribution, 



S G 

E .'. Men do not do right for the sake of themselves. 



Fallacy of illicit major. 

(6) "If an animal is a vertebrate, then it must have a 
backbone; but the books say that this animal is not a 
vertebrate, hence it cannot have a backbone." 
Since the minor premise denies the antecedent it would 
appear that the argument is invalid; yet common knowl- 
edge and common sense dictate that the conclusion is 
true. Surely no invertebrate can have a backbone. As 
a matter of fact the antecedent and consequent are 
co-extensive and therefore the hypothetical rule is not 
applicable. 



302 Hypothetical and Disjunctive Arguments 

Reduced to the categorical: 

M G 

A Vertebrates must have a backbone (Co-extensive) 



S M 

This animal is not a vertebrate, 



S G 

E .'. This animal cannot have a backbone. 



As co-extensive A's distribute their predicates the possi- 
bility of there being a fallacy of illicit major is forestalled. 
Categorically considered the argument is likewise valid. 

8. DISJUNCTIVE ARGUMENTS. 

It has been observed that a disjunctive proposition is 
one which expresses an alternative. A disjunctive syllo- 
gism is one in which the major premise is a disjunctive 
proposition. 

Illustration : 

The boy is either honest or dishonest, 
He is honest, 
.'. He is not dishonest. 

9. THE TWO KINDS OF DISJUNCTIVE ARGUMENTS. 

The two forms of disjunctive arguments are the one 
zvhich by affirming denies and the one which by denying 
affirms. The former is known by the Latin words "modus 
ponendo tollens" ; while the latter is termed the "modus 
tollendo ponens." 



The Tzuo Forms of Disjunctive Arguments 303 

Illustrations : 

( 1 ) By affirming denies. 

The defendant is either guilty or innocent, 

He is guilty, 
. ' . He is not innocent, 
or 

The defendant is either guilty or innocent, 

He is innocent, 
.*. He is not guilty. 

(2) By denying affirms. 

The defendant is either guilty or innocent, 

He is not guilty, 
.'. He is innocent, 
or 

The defendant is either guilty or innocent, 

He is not innocent, 
.'. He is guilty. 

10. THE FIRST RULE OF DISJUNCTIVE ARGUMENTS. 

It may be said that disjunctive arguments depend on 
tzuo rules. This is the first: The major premise must 
assert a logical disjunction. A logical disjunction in- 
volves two requisites; first, the alternatives must be 
mutually exclusive; second, the enumeration must be 
complete. 

Illustrations of illogical major premise. 
Terms not mutually exclusive: 

This boy is either inattentive or indolent, 
He is not inattentive, 
.*. He is indolent. 



304 Hypothetical and Disjunctive Arguments 

It is obvious that the boy might be both inattentive and 
indolent. Experience teaches that the qualities are usually 
concurrent, and to assume that the boy must be either one 
or the other is a clear case of "begging the question." 

Some logicians maintain that "either — or" signify that 
both alternatives cannot be false, but that both may be 
true. If this viewpoint were adopted, the major premise 
of the illustration would not be a case of begging the 
question. It is unnecessary to argue the point, if it is 
made perfectly clear which view is to obtain in this dis- 
cussion. Briefly stated the two points are these. First 
opinion: "Either — or" when used logically, mean that if 
the first alternative is false the second must be true, or if 
the first alternative is true the second must be false. Sec- 
ond opinion : "Either — or" when used logically mean that 
if the first alternative is false, the second must be true; 
but if the first alternative is true, the other may or may 
not be true. This treatise adopts the first opinion. With 
us all alternative arguments to be logical must be mutually 
contradictory; i. e., when one is false, the other must be 
true and when one is true the other must be false; both 
cannot be false, neither can both be true. When it is 
intended that this implication should not obtain, then 
the expressed alternative will take this form, "The boy is 
either inattentive or indolent or both." 

Other examples where the terms of the disjunctive 
may not be mutually exclusive: 

( i ) "Lord Bacon was either exceedingly studious or 
phenomenally bright." (Undoubtedly he was 
both.) 



The First Rule of Disjunctive Arguments 305 

(2) "This teacher is a graduate either of Harvard or 

of Yale." (Perhaps both.) 

(3) "The defendant is either a liar or a thief." 

(The one often leads to the other.) 

(4) "To succeed one must either seize the oppor- 

tunity as it passes or make his own." (The 
best success results from doing both.) 

Incomplete enumeration: 

The cause of the disease was either the water 

or the milk, 
It was not the milk, 
.". It was the water. 

When such an argument as this is advanced, it must be 
with the knowledge that every other alternative has re- 
ceived satisfactory investigation. Without this assurance 
one could justly claim that the disease might have been 
caused by the meat or fish supply. Complete enumeration 
means that the investigation has narrowed the facts to 
the boundary of the field covered by the alternatives. 
The fallacy of incomplete enumeration is also one of 
"begging the question." 

Other examples of a possible incomplete enumeration: 

(1) "Jones lives either in Boston or New York." 

(2) "Mary is studying either algebra or geometry." 

(3) "He either committed suicide or was lynched." 

(4) "Either the Giants or the Boston Americans will 

win the pennant." 



306 Hypothetical and Disjunctive Arguments 

11. SECOND RULE OF DISJUNCTIVE ARGUMENTS. 

The second rule is made so self evident by the first 
that there is little need of a detailed discussion concerning 
it. The rule is this : When the minor premise affirms or 
denies one of the alternatives of a logical disjunction, the 
conclusion must, in order, deny or affirm all of the others. 
To put it differently: When the "minor" affirms, the 
conclusion must deny every other alternative, and vice 
versa. When there are but two alternatives reference to 
any of the foregoing disjunctive arguments will make the 
rule clear. There may be, however, more than two 
alternatives. In such a case, if the first rule is observed 
then the second becomes applicable. 

Illustrations : 

(i) John Doe lives either in Boston, Albany, or New 
York; 
He lives in New York, 
.'. He does not live in either Boston or Albany, 
or 
He does not live in New York, 
.*. He lives in either Boston or Albany. 

(2) The season must have been either summer, or 
autumn, or winter, or spring; 
It was neither autumn, nor winter, nor spring, 
.*. It must have been summer, 
or 
It was either autumn, or winter, or spring, 
.'. It could not have been summer. 



Reduction of the Disjunctive Arguments 307 

12. REDUCTION OF THE DISJUNCTIVE ARGUMENT TO 
THE HYPOTHETICAL AND THEN TO THE CATE- 
GORICAL. 

It would seem that the laws of the disjunctive contra- 
dict those of the categorical syllogism ; for we apparently 
derive from two affirmatives a negative conclusion, and 
we also derive an affirmative conclusion when one prem- 
ise is negative. This objection is seen to be nugatory 
when the disjunctive is reduced to the categorical form. 
The reduction involves the two steps of first changing the 
disjunctive to the hypothetical form and then to the 
categorical form. The following illustrations will suffice 
to make the matter clear : 

(1) Disjunctive. 

A is either B or C 
AisB 
.*. A is not C 

Hypothetical. 

If A is B, then A is not C 
AisB 
.'. A is not C 

Categorical. 
The case of A being B is the case of A not being C 
In this case A is B 
.'. A is not C 

(2) Disjunctive. 

The defendant is either guilty or innocent ; 
He is not innocent, 
.*. He is guilty. 



308 Hypothetical and Disjunctive Arguments 

Hypothetical. 

If the defendant is guilty, then he is not innocent ; 
But he is guilty, 
.'. He is not innocent. 
Categorical. 

The case of the defendant being guilty is the 

case of the defendant not being innocent, 
In this case the defendant is guilty, 
.". In this case the defendant is not innocent. 

13. THE DILEMMA. 

The majority of us are acquainted with the dilemma as 
related to the activities of life. One is in a dilemma 
when there are two courses open to him but neither is 
particularly enticing. One is placed in a dilemma when he 
is forced to choose the lesser of two evils. For example, 
one may, without the proper equipment, be overtaken by 
a heavy rain storm; he seeks the shelter of a wayside 
shed ; the rain continues so that he is forced either to miss 
his train, or to endure the discomfort of a drenching. 
Thus the logical dilemma limits one to a choice between 
alternatives, either one of which might well be avoided. 

Definition. 

The dilemma is a syllogism in which the major premise 
consists of tzuo or more hypothetical propositions, while 
the minor premise is a disjunctive proposition. 

It being a combination of hypothetical and disjunctive 
propositions the dilemma is sometimes appropriately re- 
ferred to as the "hypothetico-disjunctive" argument. The 



The Dilemma 309 

order of the premises is indifferent, yet it seems to be 
more natural to use the hypothetical first; thus the 
definition. 

14. FOUR FORMS. 

The four forms of the dilemma are the simple con- 
structive, the simple destructive, the complex constructive, 
and the complex destructive. The following symboliza- 
tions illustrate these four kinds : 

Simple Constructive Dilemma. 

If A is B, W is X; and if C is D, W is X, 

But either A is B or C is D, 

Hence W is X. 
This is termed a simple dilemma because there is but one 
consequent; namely, W is X. The conclusion being 
affirmative makes it constructive. 

Simple Destructive Dilemma. 

If A is B, W is X; and if A is B, Y is Z, 
But either W is not X or Y is not Z, 
Hence A is not B. 
This is simple because there is but one antecedent, A is 
B, and destructive because the conclusion is negative. 

Complex Constructive Dilemma. 

If A is B, W is X; and if C is D, Y is Z, 
But either A is B or C is D, 
Hence either W is X or Y is Z. 
This is complex because there are two antecedents and 



310 Hypothetical and Disjunctive Arguments 

two consequents ; constructive, inasmuch as the conclusion 
is affirmative. 

Complex Destructive Dilemma. 

If A is B, W is X; and if C is D, Y is Z, 
But either W is not X or Y is not Z, 
Hence either A is not B or C is not D. 
This is complex because there are two antecedents as well 
as two consequents, and destructive because the conclusion 
is negative. Briefly : ( i ) A simple dilemma is one where 
either the antecedent or consequent is repeated; whereas 
if neither is repeated the dilemma is complex. (2) A 
constructive dilemma contains an affirmative conclusion; 
while a destructive dilemma uses a negative conclusion. 
(3) A simple dilemma has as its conclusion a categorical 
proposition ; whereas the conclusion of a complex dilemma 
is always disjunctive. 

If the number of antecedents and consequents be in- 
creased, a trilemma, tetralemma, etc., may result. 

Illustration — Trilemma. 

If A is B, W is X; and if C is D, Y is Z; 

and if E is F, U is V, 
But either A is B, or C is D, or E is F, 
Hence either W is X, or Y is Z, or U is V. 
Some authorities define a dilemma as a syllogism in 
which the "major-hypothetical" has more than one ante- 
cedent while the "minor" must be disjunctive. This view- 
point necessarily excludes the second form or the simple 
destructive dilemma. The weight of authority, however, 
appears to favor the classification here recommended. 



Rule Involved in Dilemmatic Arguments 311 



15. THE ONE RULE INVOLVED IN DILEMMATIC ARGU- 

MENTS. 

Since the major premise of the dilemma is hypothetical, 
the rule for testing such would of necessity be the hypo- 
thetical rule; namely, "The minor premise must either 
affirm the antecedent or deny the consequent." As this 
rule and the fallacies incident to it have been treated in 
detail, further discussion is unnecessary. 

16. ILLUSTRATIVE EXERCISE TESTING DISJUNCTIVE 

AND DILEMMATIC ARGUMENTS. 

(1) If the arithmetic contains useful facts, it will help 
to good citizenship ; and if it trains the powers 
of reason, it will help to good citizenship, 
But the arithmetic either contains useful facts or 

trains the powers of reason, 
Hence it will help to good citizenship. 
This is a simple constructive dilemma in which the minor 
premise affirms the antecedents. The argument is, there- 
fore, valid since it conforms to the rules of the hypo- 
thetical syllogism. The fact that the minor premise may 
not be a perfect disjunctive does not invalidate the con- 
clusion, inasmuch as it is perfectly obvious that if the 
arithmetic fulfilled both the requirements of the ante- 
cedents, the conclusion would still obtain. It may, there- 
fore, be inferred that if the dilemma conforms to the 
rules of the hypothetical argument, it is valid, though the 
disjunctive proposition which it contains may not be 
strictly logical. 



312 Hypothetical and Disjunctive Arguments 

(2) A man is either temperate or intemperate; and, as 
I have seen you drunk several times, I conclude that you 
are intemperate. 

Arranged logically. 

A man is either temperate or intemperate, 
You are not temperate, 
.'. You are intemperate. 

It would seem that the major premise is a logical disjunc- 
tive, since temperate and intemperate indicate that the 
alternatives are mutually exclusive and the enumeration 
complete. And since the minor premise denies one 
alternative while the conclusion affirms the other, we may 
infer that the argument is valid. 

(3) If a man is honest, he will either pay his debts or 
explain; but this fellow paid no heed to the repeated 
notifications. 

Arranged logically. 

If a man is honest, he will pay his debts ; and if he 
is honest, he will explain in case he cannot pay, 
This man neither paid his debt, nor explained, 
.*. This man is not honest. 
This is a simple destructive dilemma, and since the minor 
premise denies the consequents it is valid. 

(4) A voter must either favor protection or free 
trade; and since you do not favor protection, you must 
be a free trader. The disjunctive is not logical as one 
might believe in universal reciprocity. The argument is, 
therefore, invalid. Why? 



Illustrative Arguments 313 

(5) If a man were loyal, he would not be unduly 
critical ; and if he were wise, he would not be too loqua- 
cious; but I find this clerk has been both unduly critical 
and too loquacious ; hence I consider that he has been not 
only unwise but strikingly disloyal. 

This complex dilemma is valid since the minor premise 
denies the two consequents. 

17. ORDINARY EXPERIENCES RELATED TO THE DIS- 
JUNCTIVE PROPOSITION AND HYPOTHETICAL 
ARGUMENT. 

( 1 ) One desires to take a certain trip which involves 
various routes; information from time tables reveals the 
fact that there are three routes A, B, and C. Concerning 
the conditions of the journey the most important factor is 
the matter of comfort. Further investigation makes evi- 
dent that route B will be the most comfortable one, and 
consequently is the route selected. Putting this ordinary 
experience in argumentative form gives the following : 

The route is to be either A, or B, or C ; 

I will take route A ; if it is the most comfortable ; 

(co-extensive) 
A is not the most comfortable route, 
Hence I will not take route A. 
If B is the most comfortable route, I will take it; 
B is the most comfortable route, 
Hence I will take route B. 

(2) The symptoms suggest either malarial or typhoid 
fever; the physician is undecided till a blood test makes 
evident that it is not typhoid. 



314 Hypothetical and Disjunctive Arguments 

Considered argumentatwely. 

This disease is either malarial or typhoid fever ; 
If it is typhoid, the blood will reveal certain evidences ; 
But the blood does not reveal these evidences, 
Hence the disease is not typhoid. 

(3) The natural bent of the youth suggests the pro- 
fession of either the ministry or teaching. He finally 
decides to follow the one in which he can best serve his 
fellows. This, after mature deliberation, appears to him 
to be the work of the teacher. Thrown into the form of 
an argument the following results: 

I am best fitted for either the pulpit or the school- 
room; 
If the schoolroom furnishes the richest field for help- 
ing my fellows, I will choose that work ; 
The schoolroom does appear to furnish such a field, 
Hence I will choose the work of the teacher. 

It would appear from these ordinary experiences that 
frequently we are brought face to face with a choice of 
alternatives which are not unattractive, as in the case of 
the dilemma. Moreover, some condition suggests itself 
which, if proved or disproved, will lead to a choice of one 
of these alternatives. Such circumstances when thrown 
into the form of an argument present a disjunctive prop- 
osition followed by a hypothetical argument. To put 
it differently: Often in our daily affairs a most prominent 
limiting condition induces us to select one out of several 
alternatives. These alternatives are not dilemmatic in 
nature. 



Outline 315 



18. OUTLINE. 



Hypothetical Arguments, and Disjunctive Arguments In- 
cluding the Dilemma. 

(1) Three kinds of arguments 

Categorical, hypothetical, disjunctive. 

(2) Hypothetical arguments 

Denned, illustrated. 

(3) Antecedent and consequent. 

How determined, illustrations. 

(4) Two kinds of hypothetical arguments 

Constructive, destructive, illustrations. 

(5) Rule and two fallacies of the hypothetical argument. 

Illustrations and application of rules. 
Fallacy of denying antecedent. 
Fallacy of affirming consequent. 
Co-extensive hypotheticals. 

(6) Hypothetical arguments reduced to the categorical form. 

Rule, illustrations. 

Hypothetical and categorical arguments compared. 

(7) Illustrative exercises testing hypothetical arguments of 
all kinds. 

(8) Disjunctive arguments. 

Defined, illustrated. 

(9) Two kinds of disjunctive arguments. 

By "affirming denies," by "denying affirms." Illus- 
tration. 

(10) First rule. 

Stated, illustrated. 

(11) Second rule 

Stated, illustrated. 

(12) Reduction of disjunctive argument 

Two steps. 

(13) The dilemma 

Definition. 

(14) Four forms of dilemmatic arguments 

Simple constructive, simple destructive, 
Complex constructive, complex destructive. 
Illustrations. 

(15) The rule. 



316 Hypothetical and Disjunctive Arguments 

(16) Illustrative exercises testing disjunctive and dilemmatic 
arguments. 

(17) Ordinary experiences related to the disjunctive propo- 
sition and hypothetical argument. 

19. SUMMARY. 

(1) Just as there are three kinds of propositions so there are 
three kinds of arguments; namely, categorical, hypothetical, dis- 
junctive. 

(2) Categorical syllogistic arguments are those in which all 
of the propositions are categorical. 

Hypothetical syllogistic arguments are those in which the 
major premise is hypothetical. 

In contradistinction to disjunctives, hypothetical arguments 
may be referred to as "conjunctive". 

(3) The hypothetical proposition is composed of antecedent 
and consequent; the former being the limiting condition; while 
the latter is the direct assertion. As the words indicate the ante- 
cedent usually precedes the consequent. The signs of the ante- 
cedent are "if," "though," "unless," "suppose," "granted that," 
"when," etc. 

(4) The two kinds of hypothetical syllogisms are the con- 
structive and destructive; the former is involved when the minor 
premise affirms the antecedent; the latter when the minor 
premise denies the consequent. These two kinds are sometimes 
referred to as "modus ponens" and "modus tollens" respectively. 

(5) Out of the four possible hypothetical syllogisms only two 
are valid as investigation proves this rule : The minor premise 
must affirm the antecedent or deny the consequent. In the case 
of the hypothetical proposition being co-extensive, the rule does 
not apply. 

(6) Hypothetical arguments may be reduced to the categor- 
ical by contracting the antecedent of the hypothetical proposition 
to form the subject-term, and by contracting the consequent of 
the hypothetical proposition to form the predicate-term of the 
major premise of the categorical syllogism. If it is necessary, 
supply a new minor term. 

Denying the antecedent is a matter of illicit major; whereas 



Summary 317 

affirming the consequent is equivalent to undistributed middle, 

(7) Hypothetical arguments may be tested by following this 
outline : 

(1) Arrange logically. (2) Determine antecedent and 
consequent. (3) Apply hypothetical rule. (4) Re- 
duce to categorical form. (5) Apply categorical 
rules. 

(8) A disjunctive syllogism is one in which the major premise 
is a disjunctive proposition. 

(9) The two kinds of disjunctives are those which "by 
affirming deny" and those which "by denying affirm." 

(10) In testing disjunctive arguments there are two rules in- 
volved: First, "The major premise must assert a logical dis- 
junction." This necessitates the two requisites "the alternatives 
must be mutually exclusive" and the "enumeration must be 
complete." The two opinions relative to the nature of an alterna- 
tive assertion are, first, if one is false, the other must be true and 
vice versa; and second, if one is false, the other must be true, 
but both may be true. The first is adopted in this discussion. 

Second. The second rule involved is "When the minor premise 
affirms or denies one of the alternatives of a logical disjunctive 
the conclusion must deny or affirm all of the others." 

(11) Subjecting the disjunctive arguments to the categor- 
ical test gives evidence to the close relation existing between 
the two forms. A logical disjunctive proves to be logical when 
reduced to the categorical. The reduction entails the two steps, 
first, reduce to the hypothetical ; second, reduce to the categorical. 

(12) The logical meaning of the dilemma is suggested by the 
popular conception. One is said to be in a dilemma when two 
courses are open to him, neither of which is specially attractive. 

A logical dilemma presents two alternatives either one of 
which might well be avoided. 

The major premise of the dilemma is hypothetical; while the 
minor is disjunctive. 

(13) The four forms of the dilemma are the simple construc- 
tive, the simple destructive, the complex constructive and the 
complex destructive. 

(14) The dilemma is subject to the hypothetical rule which 



318 Hypothetical and Disjunctive Arguments 

is, "The minor premise must either affirm the antecedent or deny 
the consequent." 

(15) The minor premise need not be a logical disjunctive pro- 
vided the major conforms to the hypothetical rule. 

(16) Frequently when ordinary experiences are reduced to 
augmentative form they present a disjunctive proposition fol- 
lowed by a hypothetical argument. 

20. REVIEW QUESTIONS. 

(1) Relate the three kinds of arguments to the three general 
kinds of propositions. 

(2) Define and illustrate the hypothetical argument. 

(3) Explain the term conjunctive with reference to hypo- 
thetical arguments. 

(4) Explain and illustrate antecedent and consequent in 
hypothetical arguments. 

(5) Select from the following the antecedent and consequent: 
(1) "I usually succeed when I try." (2) "I will not 

undertake it unless you guarantee half of the 
sum needed." (3) "Though I speak with the 
tongues of men and of angels, and have not char- 
ity, I am become as sounding brass or a tinkling 
cymbal." 

(6) Illustrate the two kinds of hypothetical syllogisms which 
are valid. 

(7) State and explain the rule to which hypothetical argu- 
ments must conform. 

(8) State and exemplify the one exception to the hypothetical 
rule. 

(9) Explain how hypothetical arguments may be reduced to 
the categorical form. Illustrate. 

(10) Show by illustration that denying the antecedent is 
equivalent to illicit major, while affirming the consequent is 
equivalent to undistributed middle. 

(11) Reduce to the categorical form and test: 

"If Napoleon had possessed more of the spirit of Wash- 
ington, he would have been less famous but a better 
man than he was; but he did not possess the spirit of 
the "Father of His Country." 



Review Questions 319 

(12) Test according to outline the following hypothetical argu- 
ments : 

(1) "If it be a good thing to have faith, then certainly 
he who believes in the bible of a pagan has faith 
and must have a good thing." 

(2) "If a 10-inch charge burst inside of a tank, there 
would be nothing left of the tank. It would be 
blown into small pieces." 

(3) "If the plate found had been originally on the out- 
side of the ship, I should have judged that there 
must be green paint on it, but I could not find green 
paint on that part of the ship." 

(4) "If I mistake not, you are the man who did not pay 
me for that pair of shoes. I am sure that you are 
the man as I never forget a face." 

(5) "If the maxim 'Early to bed and early to rise makes 
one healthy, wealthy and wise' were true, I would 
have been a millionaire long ago." 

(13) Define and illustrate a disjunctive argument. 

(14) Exemplify the two kinds of disjunctive arguments. 

(15) What is meant by a logical disjunction? 

(16) "The alternatives must be mutually exclusive." Explain 
this, illustrating fully. 

(17) Cite cases where the enumeration is not complete. 

(18) State in complete form both of the rules to which all 
disjunctive arguments must conform. 

(19) Show by illustration how the disjunctive syllogism may 
be reduced to the categorical. 

(20) Define and illustrate the dilemma. 

(21) Give examples, using symbols, of the four dilemmatic 
forms. Explain why these forms are so named. 

(22) Why does the hypothetical rule apply to the dilemmatic 
syllogism ? 

(23) Test the validity of the following: Give reasons. 

(1) "If a substance is solid it possesses elasticity and 

so also it does if it be a liquid or gaseous ; but all 
substances are either solid, liquid or gaseous; 
therefore, all substances possess elasticity." 

(2) "If men were prudent, they would act morally for 



320 Hypothetical and Disjunctive Arguments 

their own good; if benevolent, for the good of 
others. But many men will not act morally, either 
for their own good or that of others; such men, 
therefore, are not prudent or benevolent." 

(3) "If the majority of those who use public houses 
are prepared to close them, legislation is unneces- 
sary; but if they are not prepared for such a 
measure, then to force it upon them by outside 
pressure is both dangerous and unjust." 

(4) "The man is either a liar or a fool and in either 
case he is beneath my attention." 

(5) "Either he is sincere or else he is the most astute 
impostor the world has ever produced; for me I 
prefer to think him sincere." 

(24) Explain the relation that many experiences appear to 
bear toward an argument introduced by a disjunctive proposi- 
tion and followed by a hypothetical syllogism. Illustrate. 

21. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) May both premises of a hypothetical argument be hypo- 
thetical propositions ? Explain. See Fowler p. 115. 

(2) Which of the two is valid ? Explain. 

(1) If A is B, C is D (2) If A is B, C is D 

If A is B, E is F If C is D,.E is F 

.*. If C is D, E is F .*. If A is B, E is F 

(3) Show by circles that two of the possible four hypothetical 
arguments are invalid. 

(4) What categorical rules does the hypothetical argument 
seem to violate? Explain. 

(5) Originate a hypothetical syllogism whose antecedent and 
consequent are both negative. Test its validity. 

(6) Originate a co-extensive hypothetical argument and show 
that four valid syllogisms may be derived from it. 

(7) Explain by word and illustration the two meanings which 
may be attached to "either-or." 

(8) If we accepted the opinion that both alternates of a dis- 
junctive may be true, which kind of disjunctive argument would 
it invalidate ? 



Questions for Origmal Thought 321 

(9) In a logical disjunction what law of thought is involved ? 
Explain. 

(10) Why do the laws of the disjunctive iseem to contradict the 
categorical rules ? Explain fully. 

(11) Show by drawing on common experience that a logical 
dilemma is closely related to the popular conception of 
dilemma. 

(12) Illustrate by symbols and then place in good English 
a pentalemma. 

(13) State a definition of a dilemma which excludes the simple 
destructive form. 

(14) Give a common experience which, when thrown into 
argumentative form, results in a disjunctive proposition fol- 
lowed by a hypothetical syllogism. Coin a name for such a 
combination. 



CHAPTER 16. 

THE LOGICAL FALLACIES OF DEDUCTIVE REASONING. 

1. A NEGATIVE ASPECT. 

It has been remarked that "Logic as a science makes 
known the laws and forms of thought and as an art sug- 
gests conditions which must be fulfilled to think rightly." 
In recent chapters we have discussed the second aspect 
of the definition ; in these we have attempted to answer 
the question, "What rules must be followed in order to 
reason correctly?" We are now ready to treat the same 
aspect from a negative point of view namely, what 
errors must be avoided in order to reason correctly? 
What are the fallacies which we must strive to avoid in 
our own thinking, and attempt to correct in the thinking 
of others? 

2. PARALOGISM AND SOPHISM. 

"Fallacy" comes from the Latin fallacia, meaning de- 
ceptive or erroneous, and therefore a fallacy in logic is 
any error in reasoning which has, an appearance of cor- 
rectness. If the writer or speaker is himself deceived by 
the fallacy, then such is called a Paralogism; but if the 
fallacy is committed by him for the expressed purpose of 
deceiving others, then such becomes a Sophism. During 
the time of the Schoolmen the Sophism was in such high 
repute that it required even a Socrates to puncture this 
ignominious bubble of vain trickery. In fact, Socrates, 
the greatest of all pagan educators, led the crusade which 

322 



Paralogism and Sophism 323 

has relegated to the "logical dust bin" the notion that 
skill m the art of framing sophisms is a scholarly accom- 
plishment. Many believe modern sophistry to be the chief 
social and commercial evil of the day, and to Socrates 
must be given the credit for teaching us to look upon 
those who would practice sophism with righteous indigna- 
tion and pronounced disgust. However, paralogism and 
not sophism is the more legitimate field for the student 
of logic; his problem being, "What are the common 
errors which I, as a writer and speaker, must strive to 
avoid ? 

3. A DIVISION OF THE DEDUCTIVE FALLACIES. 

The mistakes of induction will occupy our attention in 
a later chapter. We are now concerned with the fallacies 
of deduction. Any classification or division of the de- 
ductive fallacies must of necessity be faulty. Even the 
labors of Aristotle in this regard are now pronounced 
crude and unsatisfactory. This is due to the divergence 
of opinion as to the signification of some of the fallacies, 
as well as to the fact that no division is free from the 
fault of an overlapping of the species. As a result of 
this lack of unanimity in definition and lack of ability in 
making the species mutually exclusive, any division of 
the deductive fallacies must be more or less illogical. 

Aristotle divides the fallacies of deduction into two 
groups: (1) Fallacies in dictione, or formal fallacies. 
(2) Fallacies extra dictionem, or material fallacies. This 
division has received universal approval and though many 
distinctions made by him have been abandoned, yet most 
logicians retain his phraseology. Since many of the tech- 



324 The Logical Fallacies of Deductive Reasoning 

nical terms which Aristotle used have lived through the 
generations under the conventional meaning which he 
assigned to them, it becomes less confusing to adhere 
as closely as possible to these terms. Therefore, in the 
attending division only those changes have been made 
which progress and experience have forced upon us. 
What remains of this chapter will be devoted to ex- 
plaining these fallacies as they appear in this division. 
For the sake of clearness and definiteness it is strongly 
recommended that the student study the outline exten- 
sively enough to be able to reproduce it. 



Fallacies. 



Formal {In dictione) 

1. Opposition 



1. Immediate 
inference' 



2. Categorical 
arguments 



3. Hypothetical 
arguments 



2. Obversion 

3. Conversion 

4. Contraversion 

5. Four terms 

6. Undistributed 

middle 

7. Illicit major 

8. Illicit minor 

9. Negative 

premises 

10. Particular 
premises 

11. Denying the 

antecedent 

12. Affirming 
the conse- 
quent 



4. Disjunctive p3. Illogical 
arguments I disjunction 



1. In Language 
Equivocation 



Material {In dictionem). 

1. Ambiguous 
middle 

2. Amphibology 

3. Accent 

4. Composition 

5. Division 

6. Figure of 
speech 



1. Accident 

2. Converse 

accident 

3. Irrelevant 

conclusion 

4. Non sequitur 

5. False cause 

6. Complex 

question 

7. Begging the 

question 



2. In Thought 
Assumption 



General Divisions Explained 325 

4. GENERAL DIVISIONS EXPLAINED. 

The formal fallacies are those which concern the form 
of the argument rather than the meaning. These fallacies 
arise from an improper use of words as abitrary signs 
of thought, not from any inconsistency in the thought 
itself. To commit a formal fallacy we must violate 
one of the specific rules of logic. For this reason the 
formal fallacies are easier of comprehension. Moreover, 
because of this definiteness logicians are better able to 
come to some agreement as to their content and import. 
Classing the fallacies of immediate inference as formal is 
somewhat of an innovation ; but since they occur because 
of the breaking of certain definite rules, and since imme- 
diate inference is a matter of changing the form without 
altering the meaning, we believe there is some justification 
for this position. Some would class "immediate in- 
ference" fallacies with the material fallacies of language. 

The material fallacies are fallacies of meaning and not 
of form. They are those arising from inconsistency in 
thought, and from imperfect ways of interpreting this 
thought as it appears in language. No very specific rules 
of logic are violated by them and for this reason there 
are those who would entirely eliminate the material falla- 
cies from the field of logic. But since thought is even 
more subtle than form in its deceitful machinations, we 
believe that the material fallacy calls for special attention 
on the part of the logician. 

Material fallacies are divided into two kinds. First, 
those which have reference to wrong thinking, or falla- 
cies in thought; and, second, those which are due mainly 



326 The Logical Fallacies of Deductive Reasoning 

to an incorrect interpretation of words, or fallacies in 
language. The former result from inconsistency and un- 
reasonableness in thought, whereas the latter come from 
lack of precision in expression. 

5. FALLACIES OF IMMEDIATE INFERENCE. 

Fallacies of immediate inference arise from some vio- 
lation of the rules which this topic enunciates. 

(1) Opposition. 

Among other statements opposition posits these two: 
( 1 ) When the particular is true its opposing universal is 
indeterminate; (2) A universal negative does not neces- 
sarily contradict a universal affirmative. 

These signify that neither an A nor an E must be 
assumed to be true when the corresponding I or O is 
true, and that E may not always contradict A,, nor O 
contradict I. 
Illustrations of Fallacies of Opposition. 

( 1 ) Since some men are wise, then I may conclude that 
all men are wise. (2) I have contradicted his statement 
"all men are honest" by proving that no men are honest. 

There is little difference between fallacies like ( 1 ) and 
fallicies of converse accident. Concerning illustration (2), 
both statements are false ; but to contradict we know that 
if one is false, the other must be true. 

(2) Obversion. 

"Two negatives are equivalent to one affirmative," is 
the principle underlying obversion. The most common 
fallacy in obversion springs from using one negative 
instead of two. 



Fallacies of Immediate Inference 327 

Illustrations of Fallacious Obversion. 

(a) Original: Some men are not wise. Obverse: (in- 
correct) Some men are wise. 

(b) Original : All true teachers are just. Obverse : (in- 
correct) All true teachers are not just. 

(3) Conversion. 

Conversion involves the interchanging of the subject 
and predicate of a proposition without affecting the dis- 
tribution ; in consequence the usual fallacy incident to this 
interchange is distributing an undistributed term. 

Illustrations of Fallacy of Conversion. 

(a) Original: All fixed stars are heavenly bodies. 
Converted: (incorrectly) All heavenly bodies are fixed 
stars. 

(b) Original: Some men are not wise. Converted: 
(incorrectly) Some wise beings are not men. 

(4) Controversion. 

As this process involves the two steps of obversion and 
conversion, fallacies appertaining to contraversion would 
relate to these two steps. 

Illustrations of Fallacies of Contraversion. 

(a) Original: No honest man fails to pay his debts. 
Contraverted : (incorrectly) Some who do not pay their 
debts are honest men. 

(b) Original: Some animals are quadrupeds. Contra- 
verted: (incorrectly) Some not-quadrupeds are not 
animals. 

The formal fallacies of categorical, hypothetical, and 
disjunctive arguments have received detailed treatment in 



328 The Logical Fallacies of Deductive Reasoning 

chapters n, 14 and 15; we may, therefore, devote our 
attention to the material fallacies without further delay. 

6. FALLACIES OF LANGUAGE. (Equivocation.) 

These are the fallacies of double meaning. It is known 
that an equivocal term is one which permits two or more 
interpretations ; similarly a proposition which admits of 
two or more interpretations may be denominated equiv- 
ocal. Thus the term equivocation has come to stand for 
all errors in language resulting from a possibility of more 
than one interpretation. This justifies the position of 
referring to all of the six fallacies in language as fallacies 
also of equivocation. 

( 1 ) Ambiguous middle. 

Ambiguous middle explains itself. It is the fallacy of 
giving to the middle term a double meaning. In form the 
argument may contain but three terms, yet in meaning 
there are in reality four terms. For this reason am- 
biguous middle and the fallacy of four terms appear to 
be about one and the same thing; but in this treatment 
we shall regard them as mutually exclusive, and this is 
the distinction : 

Invalid arguments of "ambiguous middle" have only 
three terms in form but four terms in meaning. This 
signifies that the middle term though identical in form is 
given a double meaning. 

Invalid arguments of "four terms" always have four 
terms in both form and meaning; they are "logical 
quadrupeds" in every sense of the word. 



Fallacies of Language 329 

Illustrations. 
Ambiguous middle. 

(a) "Necessity is the mother of invention," 
Bread is a necessity, 

.'. Bread is the mother of invention. 

(b) "Nothing is better than wisdom," 
Dry bread is better than nothing, 

.'. Dry bread is better than wisdom. 

(c) A church is a force for good in any community, 
A slate roof is good for a church, 

.'. A slate roof is a force for good in any community. 

Fallacies of four terms. 

(a) All true teachers are just, 
John Doe is an educator, 

.'. John Doe is just. 

(b) Milk is nourishing, 

This substance is a white fluid, 
.'. This substance is nourishing. 

(c) Thieves should be imprisoned, 

This man has taken what does not belong to him, 
.*. This man. should be imprisoned. 

In the "four-term" fallacies, observe that the four 
terms occur in the premises. When a fourth term is 
introduced in the conclusion, the material fallacy of 
non sequitur has been committed. 

(2) Amphibology (or amphiboly). 

Amphibology is a fallacy resulting from an ambiguous 



330 The Logical Fallacies of Deductive Reasoning 

proposition rather than from the ambiguity of any 
particular term. The fallacy of amphibology is committed 
when the spoken or written proposition conveys more 
than one meaning. The ancient oracles indulged in this 
sort of fallacy, the reason for such indulgence being 
obvious ; the oracles were not too positive as to the out- 
come of their prognostications, and therefore were espe- 
cially careful to cover every emergency. 

A careless use of relative clauses and prepositional 
phrases often results in the fallacy of amphibology. 

Illustrations of the Fallacy of Amphibology. 

(a) "You the enemy will slay." 

(b) "The Duke yet lives that Henry shall depose.'' 

(c) "Wanted a piano by a young lady made of 

mahogany." 

(d) "You your father will punish." 

(3) Accent. 

This fallacy springs from placing undue emphasis on 
some word or group of words. Naturally such accen- 
tuation may convey a meaning entirely foreign to the 
author's intent. Newspapers are guilty of this fallacy 
when they select a few words from a speech and use 
them as headlines without further explanation. A poli- 
tician may quote a sentence uttered by an opponent and 
fail to relate it to what preceded or followed. A car- 
toonist may arouse the prejudice of public opinion by 
giving ridiculous emphasis to some idiosyncracy possessed 
by the subject of his attack. 



Fallacies of Language 331 

Illustrations of Fallacies of Accent. 

(a) "Thou shalt not bear false witness against 

thy neighbor." 
By giving undue emphasis to neighbor, the notion is 
clearly conveyed that one may bear false witness against 
all who are not neighbors. 

(b) "You must not crib when taking my exami- 

nations. 

(c) What the "Spellbinder" said. 

"I may say, as a side remark, that the labor unions 
are guilty of developing a nation of shirks, when they pro- 
hibit a phenomenally efficient workman from doing his 
best." "I do not wish to be misunderstood in this." "I 
believe in labor unions but in this particular they are 
dead wrong." 

What the newspaper reported. 

(Headline) "The Labor Union Scored as a Training 

School for Shirks." " said in his speech in 

Hall that the Union was responsible for the development 
of a nation of shirks." "A good man," said he, "is not 
permitted to do his best work." 

(4) Composition. 

The fallacy of composition is committed when it is 
assumed that what is true distributively is likewise 
true collectively. A term is used in a distributive sense 
when it is applied to each individual of the class; whereas 
a term is used in a collective sense when it is applied to 
the class considered as one whole. "All" meaning each 
one considered separately and "all" meaning the whole 
furnishes a frequent pitfall for this fallacy. 



332 The Logical Fallacies of Deductive Reasoning 

Illustrations of the Fallacy of Composition. 

(a) "Every member of the team is a star player; 

hence I expect that the entire aggregation 
will be a winner." 

(b) "All the men of the jury are fair minded; 

therefore we have good reason for sup- 
posing that the jury's verdict will be in 
accord with the rules of justice." 

(c) "Thirteen and twenty-three are odd numbers ; 

thirty-six is equal to thirteen and twenty- 
three ; hence thirty-six is an odd number." 

(d) "All the angles of a triangle are less than 

two right angles; hence the angles X, Y 
and Z are less than two right angles." 

(e) In governmental affairs the assumption, that 

a law which benefits one section will 
benefit all, is a fallacy of composition. 
( 5 ) Division. 

The fallacy of division is committed when it is as- 
sumed that what is true collectively is true distributively. 
Division is the converse of composition. Composition is 
a fallacious procedure from a distributive to a collective 
use; while division is a fallacious procedure from a 
collective to a distributive use. The fallacy of division 
may be illustrated by giving the converse of the illus- 
trations under composition: 

(a) "The team is a star playing team ; and since 
Smith is the 'first baseman' of the team, 
he must be a star player." 



Fallacies of Language 333 

(b) "The jury rendered a just decision; hence 

the foreman is a fair minded man." 

(c) Thirty-seven is an odd number, 

Nine and twenty-eight are thirty-seven, 
.'. Nine and twenty-eight are odd numbers. 

(d) All the angles of a triangle are equal to two 

right angles, 
A is an angle of a triangle, 
.'. A is equal to two right angles. 

(6) Figure of Speech. 

This fallacy results from assuming that words of the 
same root have the same meaning. Since the same root- 
word may be used as a noun, verb, adjective, etc., it does 
not follow that in these various forms it retains a com- 
mon meaning. "Address" as a noun and "address" as a 
verb convey two distinct meanings. 

The following are examples of this fallacy: 

(a) No designing person should be trusted, 
This architect is a designer, 

.'. This architect should not be trusted. 

(b) Justifiable investigation is wise, 
This man is a just investigator, 

.'. This man is wise. 

These fallacies are not classed as those of "four terms" 
because two terms so closely resemble each other in 
form, and yet they are not fallacies of ambiguous mid- 
dle: since the middle terms are not identical in form. 



334 The Logical Fallacies of Deductive Reasoning 

7. FALLACIES IN THOUGHT. 

The fallacies in thought arise through a tendency to 
assume as true that which demands further proof. Any- 
one who is more anxious to be right than to win will 
make sure that nothing has been taken for granted which 
should receive further investigation, or that no truth has 
been given a presumptuous twist in order to make it fit 
the particular case under discussion. Because these er- 
rors in thought may be attributed chiefly to undue as- 
sumptions, we may denominate them as the fallacies of 
assumption. 

(i) Accident. 

The fallacy of accident occurs when one reasons from 
a general truth to an accidental case. Doctrinaires and 
theoretic enthusiasts are partial to this fallacy. It is so 
easy to lay down a general formula or remedy and then 
attempt to apply it to every accidental circumstance. 
Grandmother with her catnip tea and mustard plaster, 
however we may cherish the memory of the dear old 
soul, was nevertheless guilty of the fallacy of accident. 
Applying maxims and proverbs to particular instances is 
still another way of committing the fallacy. 
Examples of Fallacies of Accident. 

(a) "Honesty is the best policy," thinks the 

physician as he reveals the cold, hard 
truth to his patient and thus shortens the 
patient's life. 

(b) Spirituous liquor in excess acts as a poison, 

and therefore should not be used to re- 
suscitate an extreme case. 



Fallacies of Thought 335 

(c) "What is bought in the market is eaten; 

raw meat is bought in the market ; there- 
fore it is eaten." 

(d) "Early to bed and early to rise makes one 

healthy, wealthy and wise." I shall prac- 
tice this for ten years and by that time 
hope to be healthy, wealthy and wise. 

(e) John has earned the enviable (?) reputation 

of being the "worst boy in school," hence 
he is going to be the worst boy in "my 
grade." 

(f) Mary is an inveterate whisperer; and since I 

know that some one is whispering, I am 
sure that that some one is Mary. 

(g) Being a convict, he is not to be trusted. 

(2) Converse Accident. 

As the title implies this is the fallacy of reasoning 
from an accidental case to a general truth. Illustrations : 

(a) "John has been a bad boy to-day; and hence 

he is going to make trouble during the 
entire term." 

(b) "This food is good for hens; and hence it 

is good for all domestic fowls." 

(c) "I know of several men who have been phe- 

nomenally serviceable to mankind, and 
none of these men were college trained; 
hence I conclude that college education is 
not essential to the attainment of the 
highest state of efficiency." 



336 The Logical Fallacies of Deductive Reasoning 

Relative to both accident and converse accident, it may 
be said that they obtain because all general truths, such 
as rules, principles, definitions, maxims, etc., have their 
exceptions; and it is through these exceptions that the 
two fallacies are made possible. 

Accident and Converse Accident Distinguished from 
Division and Composition. 

The fallacy of accident, we have learned, occurs when 
one reasons from a general truth to an accidental case ; 
whereas the fallacy of division obtains when one reasons 
from a collective use of a term to a distributive use; in 
both cases the procedure is from a larger unit to a 
smaller unit. Moreover, with converse accident and 
composition, the movement is from the smaller unit to the 
larger. Because of this similarity there is danger of 
confusing the two kinds of fallacies. As a matter of 
distinction between the fallacies of accident, and composi- 
tion and division the attending comparative resume may 
be of value : 

(1) Division is similar in movement to accident, 

while composition resembles converse 
accident. 

(2) A valuable cue for remembering which way 

division and accident move, is to recall 
that division in arithmetic is a procedure 
from the larger unit to the smaller, and 
therefore that division in logic would 
have the same signification. 

(3) Division and composition pertain to mathe- 



Fallacies of Thought 337 

matical wholes; while accident and con- 
verse accident relate to logical wholes. 

(4) The aggregates of division and composition 

may be counted or enumerated easily; 
while the accident and converse accident 
aggregates (or generals) are not easily 
enumerated. 

(5) Division and composition relate to logical 

terms, whereas accident and converse 
accident relate to general truths. 

(6) Division and composition use a term in a 

collective sense and then in a separate or 
distributive sense, or vice versa; accident 
and converse accident use a thought in a 
general and then in an accidental sense, 
or vice versa. 
Irrelevant Conclusion (Ignoratio Elenchi). 
The fallacy of irrelevant conclusion results when the 
argument does not squarely meet the point at issue. It is 
the fallacy of arguing to the wrong point either purposely 
or through ignorance. One in defense, who has a weak 
case, may be tempted to divert attention from the point 
in hand, realizing that a close analysis of the matter in 
dispute will tend to his undoing. In such instances (1) 
the lawyer will abuse the plaintiff, (2) the demagogue 
will tell humorous stories, (3) the teacher will take ad- 
vantage of the ignorance of the pupil, (4) the scholar will 
refer to authority and (5) the magnate will fall back 
upon the power of position and wealth. These forms of 
"rhetorical thinking" are as harmful as they are popular, 



338 The Logical Fallacies of Deductive Reasoning 

and furnish one of the chief reasons for giving to the 
common people a better understanding of "how to think" 
as well as "how not to think." 

Definite names have been given to the various forms 
of irrelevant conclusion which may be summarized as 
follows : 

Argumentum ad populum. 

This is the fallacy of appealing to the feelings, pas- 
sions and prejudices of an audience rather than to their 
good sense and powers of reason. It is probably the 
most common of the group. To excite sympathy, the 
lawyer for the defense may speak feelingly of the suffer- 
ing that an unfavorable verdict will bring to the wife 
and children of the accused. 

Argumentum ad hominem. 

Here the character of the opponent is defamed with a 
view of discrediting him with the court or audience. 
"Mud throwing" in times of political agitation is a good 
example of this fallacy. 

Argumentum ad ignorantiam. 

This fallacy comes from taking advantage of the ig- 
norance of the opponent; the fallacy assumes that the 
original supposition has been proved if one is unable to 
prove the contradictory of the original. Illustration: 
Mars is inhabited because no one is able to prove that 
Mars is not inhabited. 

Argumentum ad baculum. 

In this all argumentation is made to give way to the 
forces of personal opposition and to the power of money. 
Illustration: A political committee seating those dele- 



Fallacies of Thought 339 

gates only, who will vote their way; and, doing this, not 
from the merits of the case, but because said committee 
happen to have a sufficient number of votes to "put the 
thing through." 

Argumentum ad verecundiam. 

This fallacy comes from supposing that the whole 
thing may be settled by citing some noted authority who 
apparently substantiates the argument advanced. 

Epitome of five forms of Irrelevant Conclusion: 

( 1 ) Appealing to the audience. 

(2) Defaming the character of the opponent. 

(3) Inability to prove the contradictory. 

(4) Gaining the point by force. 

(5) Citing authority. 

Non Sequitur {False Consequent). 

This is the fallacy of deriving a conclusion which does 
not follow from the premises. The fallacy obtains when- 
ever material appears in the conclusion, which has no 
bearing on the case under discussion. "Irrelevant con- 
clusion" pertains to the establishment of the premises 
while "non sequitur" is concerned with the conclusion 
only. We know that a logical thinker constructs the 
conclusion from material already presented by the 
premises ; "Non sequitur" uses material in the conclusion 
which is found in neither premise. 

"Non sequitur" differs from the fallacy of four terms 
in that the latter uses the fourth term in the premises 
while the former introduces the fourth term in the con- 
clusion, and in a form so well obscured that it sometimes 
escapes notice. Illustration: 



34-Q The Logical Fallacies of Deductive Reasoning 

All men are thinking animals, 

Socrates was a man, 
.*. Socrates was a scholar. 
It does not follow that because a man is a thinking 
animal that he will become scholarly. 

False Cause. 

This is the fallacy of assuming that because two hap- 
penings have occurred together several times, the one is 
the cause of the other. This very common fallacy is due 
to lack of discrimination, and to the exaggerations inci- 
dent to fear and superstition. Illustrations: 

(a) Planting vegetables which grow down, such as 
the beet, during the last two days of the waxing moon 
in order to have a larger yield. So far as we know the 
moon has no influence over growing vegetables. 

(b) Thirteen seated at a table is an indication that 
one of the number will die during the year. This is one 
of the most absurd fallacies that has ever been visited 
upon an intelligent people. 

It is seen that "False Cause" is closely related to 
"Non Sequitur." 

Complex Question {Double Question). 

This fallacy obtains when an assumption is put in the 
form of a question. 

Illustrations : 

(a) A wise father who did not want to tempt beyond 
the yielding point his three-year-old son, asked, pointing 
to the scratches on the new mahogany piano, "Freddie, 
did you do that last night or this morning?" 



Fallacies of Thought 341 

(b) What caused you to desist from slandering your 
neighbors; New Year's resolutions or the preaching of 
Dominie X? 

(c) A daily paper anecdote : 

"Charles Bradlaugh, the noted English free-thinker, 
once engaged in a discussion with a dissenting minister. 
He insisted that the minister should answer questions by 
a simple yes or no, asserting that every question should 
be replied to in that manner." The reverend gentleman 
arose and said, "Mr. Bradlaugh, will you allow me to 
ask you a question on these terms ?" "Certainly," said 
Mr. Bradlaugh. "Then, may I ask, have you given up 
beating your wife?" 

Begging the Question (Petitio Principii). 

This is a fallacy of deriving a conclusion from notions 
which in themselves demand proof. 

The fallacy is not committed when the assertion is self- 
evident. It is easy to claim that our opponent is begging 
the question as soon as we see that he is getting the better 
of us. One may himself beg the question by being too 
ready to charge others with begging the question. When 
the opponent adopts premises which are commonly ac- 
cepted, he does not beg the question. One commits the 
fallacy when he seems to prove the conclusion more satis- 
factorily than he really does. This he may accomplish by 
covertly taking for granted the truth of notions which 
have not the stamp of universal approval. The fallacy of 
begging the question assumes three forms : 

(1) The assumption of an unproved premise (as- 
sumptio non probata). 



342 The Logical Fallacies of Deductive Reasoning 

In this either the major or the minor premise, or both 
may demand more substantial proof. It must be borne 
in mind, however, that the disputant must not ask for 
further proof after he has once accepted the premises, 
or after the opponent has met his demands to the satis- 
faction of commonly accepted authority. 

Examples of begging the question by assuming un- 
proved premises: 

(a) All patriotic citizens are honest at heart, 

This man charged with graft is a patriotic citizen, 
.'. This man charged with graft is honest at heart. 
"All patriotic citizens are honest at heart," is not an 
accepted truth and thus demands proof. 

(b) A famous sophism of the Greek philosopher by 
which he proved that motion was impossible, is an 
excellent illustration of an assumed premise: 

"If motion is possible, a body must move either in the 
place where it is, or in the place where it is not; 

But a body cannot move in the place where it is ; and 
of course it cannot move where it is not, 

Therefore, motion is impossible." 

Referring to this, De Morgan claims "Movement is 
change, and so a body requires tzvo places in order to 
move." A body cannot move in the place where it is, 
but must be moved from place to place. The major 
premise being assumed, this sophism illustrates the fallacy 
of begging the question. 

fc) The most subtle form of begging the question is 
an enthymeme where the suppressed premise is the one 



Fallacies of Thought 343 

assumed; e. g., "You, being a teacher, should not do as 
other people do." 

Completed and arranged the argument becomes : 
No teacher should do as other people do, 
You are a teacher, 
.'. You should not do as other people do. 
Surely the major premise demands proof. 

(2) Reasoning in a Circle {Cir cuius in probando). 
This form of begging the question occurs, "When a 

conclusion is based upon a premise which in an earlier 
stage of the argument was itself based upon this very 
conclusion." To put it in another way: Reasoning in a 
circle involves proving the truth of a conclusion by using 
a particular premise, and then proving the truth of the 
particular premise by using the conclusion. From prem- 
ise to conclusion and from conclusion to premise 
completes the circle. 

Examples of begging the question by reasoning in a 
circle: 

(a) It is wrong because my conscience pricks me, and 
my conscience pricks me because it is wrong. 

(b) "The effeminate walk shows a lack of force; 
because no forceful man walks that way." 

(c) Says Hamilton, "Plato, in his Phoedo, demon- 
strates the immortality of the soul from its simplicity; 
and in the Republic, he demonstrates its simplicity from 
its immortality." 

(3) Question Begging Epithets and Appellations. 
This is the fallacy of assuming the point at issue by 

means of a carefully selected epithet. 



344 The Logical Fallacies of Deductive Reasoning 

Scientists sometimes assume to clarify an inexplicable 
phenomenon by giving it a technical name. Politicians 
are exceedingly free with their epithets and appellations, 
and the records of religious disputes prove that the 
theologian often resorted to this device. 

Examples of begging the question by using epithets 
and appellations: 

(a) We must attribute the disease to heredity. 

(b) The candidate for governor is an animated 
feather duster. 

(c) They call him Blue Charlie. 

(d) It is the policy of the big stick. 

(e) The muck-raker seldom makes an efficient ser- 
vant of the people. 

It is seen that the use of these epithets and appella- 
tions is simply a rhetorical device for the purpose of 
creating either a favorable or unfavorable impression. 

8. OUTLINE. 

The Logical Fallacies of Deductive Reasoning. 

(1) A negative aspect of definition of logic. 

(2) Paralogism and sophism. 

Distinguished. Mission of Socrates. 

(3) A division of the deductive fallacies. 

More or less faulty. Aristotle's phraseology retained. 
Division given. 

(4) General divisions explained. 

Formal and material. Material fallacies in language 
and in thought. 

(5) Fallacies of immediate inference. 

Opposition, obversion, conversion, contraversion. 



Outline 345 

(6) Fallacies in language (also fallacies of equivocation). 

Ambiguous middle — distinguished from four terms. 

Amphibology. 

Accent. 

Composition — "all" a pitfall. 

Division. 

Figure of speech. 

(7) Fallacies in thought — (also fallacies of assumption). 

Accident. 

Converse accident. Made possible by exceptions. 

Accident and converse accident distinguished from 
composition and division. 

Comparative resume. 
Irrelevant conclusion (ignoratio elenchi). 

Argumentum ad populum. 

Argumentum ad hominem. 

Argumentum ad ignorantiam. 

Argumentum ad baculum. 

Argumentum ad verecundiam. 
Non sequitur (false consequent). 
False cause. 
Complex question. 
Begging the question (petitio principii). 

Assumption of premise. 

Reasoning in a circle. 

Question begging epithets and appellations. 

9. SUMMARY. 

(1) Logic as a science makes known the laws and forms of 
thought and as an art suggests conditions which must be 
fulfilled in order to think rightly. 

A discussion of the second phase of the definition would be 
incomplete without a consideration of the negative aspect as well 
as the positive. Such a viewpoint makes evident the question 
"What errors must be avoided in order to reason correctly?" 
An answer to this question is given under the caption of 
Logical Fallacies. 



346 The Logical Fallacies of Deductive Reasoning 

(2) A logical fallacy is any error in reasoning which has the 
appearance of correctness. 

A fallacy which deceives the writer or speaker himself is 
termed a paralogism, whereas a fallacy formed for the express 
purpose of deceiving another is denominated a sophism. 

It was the pagan teacher Socrates who taught modern thought 
to frown upon all forms of sophism; these exist to-day much as 
they did in the olden time. 

(3) Because of disagreement as to definition, and because of 
inability to prevent an overlapping of species, any logical division 
of the deductive fallacies must be faulty. 

In the division of the deductive fallacies, this treatise retains 
the phraseology and form worked out by Aristotle, so far as 
such retention is consistent with the changes incident to the 
advances of time. 

(4) Formal fallacies occur because of careless and improper 
use of words as arbitrary signs. Formal fallacies are definite 
and easy of comprehension. 

The material fallacies are due to certain inconsistencies in 
thought and to imperfect ways of interpreting language. They 
are more subtle and thus more difficult of comprehension than 
the formal fallacies. 

There are material fallacies in thought and material fallacies 
in language ; the former are due to looseness in thinking and the 
latter to lack of precision in expression. 

(5) Fallacies of opposition result most frequently from 
deriving universals from their corresponding particulars, and 
from assuming to contradict affirmative universals by negative 
universals and affirmative particulars by negative particulars. 

The common fallacy in the process of obversion consists in 
using one negative instead of two, whereas the ordinary error of 
conversion is a matter of distributing an undistributed term. 

Fallacies of contraversion must involve either those of 
obversion or conversion since the process is a combination of the 
two. 

(6) Fallacies in language, because they result from permitting 
more than one interpretation, may be also denominated fallacies 
of equivocation. 



Summary 347 

(1) Ambiguous middle is the fallacy of giving to the 

middle term a double meaning. 
The fallacy of four terms, as the name signifies, 
exists when the argument has four terms in both 
form and meaning. Ambiguous middle is a matter 
of four terms in meaning but only three in form. 

(2) The fallacy of amphibology is committed when the 
given proposition conveys more than one meaning. 
In order to maintain their prestige the ancient 
oracles made use of this fallacy. 

(3) The fallacy of accent springs from placing undue 

emphasis on some word or group of words. 
Newspaper and demagogues are prone to this error, 
that they may thus create an unfavorable impression 
towards those whom they oppose. 

(4) The fallacy of composition is committed when it is 

assumed that what is true distributively is likewise 
true collectively. "All" meaning each one and "all" 
meaning the whole class often leads to the fallacy 
of composition. 

(5) The fallacy of division is committed when it is 
assumed that what is true collectively is true 
distributively. 

Division is the converse of composition. 

(6) The fallacy of figure of speech is occasioned by 

assuming that words of the same root have the 
same meaning. 

(7) Fallacies in thought are likewise called fallacies of as- 
sumption, because of the tendency to assume as true something 
which demands further proof. 

(1) The fallacy of accident occurs when one reasons 

from a general truth to an accident case. It is the 
favored fallacy of the doctrinaire, the reformer and 
the vender of "cure-alls." 

(2) The fallacy of converse accident occurs when one 
reasons from an accidental case to a general truth. 

Both accident and converse accident are made possible 



348 The Logical Fallacies of Deductive Reasoning 

because rules, definitions, maxims, etc., have exceptions. It is 
easy to confuse division and composition with the fallacies of 
accident. Division and composition are concerned with the 
collective and distributive use of terms, whereas the fallacies of 
accident involve the use of notions in a general and accidental 
sense. The former represent notions which may be counted or 
enumerated while the latter concern notions which are logical 
rather than numerical. Composition and division involve 
"number of," accident, "meaning of." 

(3) The fallacy of irrelevant conclusion results when 

the argument does not squarely meet the point at 
issue. It is the fallacy of arguing to the wrong 
point either purposely or ignorantly. This may be 
accomplished by (1) appealing to sympathy of 
audience, (2) defaming character of opponent, (3) 
assuming that the fact is true because of inability 
to prove the contradictory, (4) gaining point by 
force, (5) citing authority. 

(4) "Non sequitur" is the fallacy of deriving a con- 

clusion which does not follow from the premises. 
It involves introducing new material in the con- 
clusion. 

(5) "False cause" is the fallacy of assuming that because 
two happenings have occurred together several 
times the one is the cause of the other. The fallacy 
is due largely to the exaggerations of fear and 
superstition. 

(6) The fallacy of complex question consists in putting 

an assumption in the form of a question. 

(7) Begging the question is the fallacy of deriving a 
conclusion from notions which in themselves demand 
proof. 

This fallacy takes the three forms of (1) the as- 
sumption of an unproved premise, (2) reasoning 
in a circle, (3) question begging epithets and 
appellations. 






Illustrative Exercises 349 

10. ILLUSTRATIVE EXERCISES IN THE TESTING OF 
ARGUMENTS IN BOTH FORM AND MEANING. 

(la) He who wilfully takes the life of another should be 
electrocuted, 
This sharp shooter has wilfully taken the life of 

another, 
Hence he should be electrocuted. 
In form we know this argument to be valid since it is in 

mood ^ A of the first figure. But as the conclusion does not 

meet with our approval, we are forced to the belief that there 
must be a material fallacy. Such proves to be the case. In the 
first instance, "Wilfully takes the life of another" is used in a 
personal, individual, selfish sense, whereas in the second instance 
the expression is used in a general, "servant-of-the-government" 
signification. The argument is, therefore, invalid, the fallacy 
being ambiguous middle. 

(lb) From the viewpoint of both form and meaning test the 
following : "Events which are not probable happen almost every 
day; but what happens every day are very probable events; 
therefore events which are not probable are very probable." 
(2a) The planets have those attributes needed in the support 
of life, 
Mars is a planet, 

Hence Mars has those attributes needed in the support 
of life. 

fA 

This is valid in form -J A in the first figure. The major pre- 

l A 

mise posits a fact which has not been proved; the argument is 
therefore invalid in meaning, the fallacy being that of begging 
the question. 

(2b) "The end of a thing is its perfection ; death is the end of 
life, therefore death is the perfection of life." 

Indicate the fallacy in the foregoing, giving reasons. 
(3a) The countries of Europe abound in beggars, 
France is a country in Europe, 
.". France abounds in beggars. 



350 The Logical Fallacies of Deductive Reasoning 

"The countries of Europe" in the major premise is used in a 
collective sense, while the same expression in the minor premise 
is used in a distributive sense. The argument is, therefore, 
invalid in meaning; fallacy of division. 

(3b) State and explain the material fallacy in the following: 

The states believe in the income tax principle; hence 
Vermont's vote will be favorable to this. 

(4a) "On general principles I believe that one is better off 
when he abstains from both tea and coffee; and this is the reason 
why I offer you a cup of hot water." 

The individual to whom the hot water was offered might have 
been in great need of a mild stimulant. Here, then, is an ex- 
ception to the general principle and the fallacy committed is 
clearly that of accident. 

(4b) "Books are a source both of instruction and amusement; 
a table of logarithms is a book; therefore it is a source both of 
instruction and amusement." Jevons. 

Designate with explanations the fallacy in the above argument. 

(5) "Twice have I started out on Friday and both times I 
had tire trouble." Fallacy of false cause. 

(6) "Where do you spend your vacation, in Palestine or 
Rome?" Fallacy of complex question. 

(7) "Of all the men of that department he seemed to be the 
most trustworthy, and I pride myself on my ability to judge men 
in this regard; but now even the police cannot find him." 

The fact that the police cannot find him has nothing to do 
with the argument. The fallacy is that of non sequitur. 

(8) "You must not whisper in my classes." Fallacy of 
accent. 

(9) "I am a Progressive because I believe in progress." 
Fallacy of figure of speech. 

(10) "I know it is true because I found it in our text book." 
Fallacy of irrelevant conclusion. 

11. REVIEW QUESTIONS. 

(1) Give the negative aspect of the second part of the 
definition of logic. 

(2) Define and illustrate the term fallacy as it is used in 
logic. 



Review Questions 351 

(3) Distinguish between a paralogism and a sophism. 

(4) Tell of the mission of Socrates. 

(5) What reasons may be given for such a divergence of 
opinion on a proper classification of the fallacies of deduction? 

(6) Give a complete outline, without explanation, of the 
deductive fallacies. 

(7) Distinguish between formal and material fallacies. 

(8) Explain the two kinds of material fallacies. 

(9) Illustrate the fallacies of immediate inference. 

(10) Why should the fallacies in language be likewise termed 
fallacies of equivocation? 

(11) Explain and illustrate ambiguous middle. 

(12) Illustrate the fallacy of amphibology. 

(13) Explain by illustration the fallacy of accent. 

(14) Explain and exemplify the fallacies of composition and 
division. 

(15) Illustrate the fallacy of figure of speech. 

(16) Give reasons for denominating the fallacies in thought 
as fallacies also of assumption. 

(17) Define and illustrate the fallacies of accident and 
converse accident. 

(18) Distinguish between the fallacies of composition and 
division and the two fallacies of accident. 

(19) "Every rule has its exception/' what has this to do with 
the fallacies of accident? 

(20) Explain and illustrate the fallacy of irrelevant 
conclusion. 

(21) Name the various ways in which irrelevant conclusion 
may be committed. 

(22) Illustrate the fallacy of non sequitur. 

(23) Explain the fallacy of false cause. 

(24) Give examples of the complex question. 

(25) How may the teacher use the complex question to 
advantage ? 

(26) Explain the fallacy of begging the question. 



352 The Logical Fallacies of Deductive Reasoning 

(27) Illustrate the three forms of begging the question. 

(28) From the viewpoint of form and meaning, test the 
validity of the following: 

(1) "No soldiers should be brought into the field who 

are not well qualified to perform their part; none 
but veterans are well qualified to perform their part, 
therefore, none but veterans should be brought into 
the field." Whately. 

(2) "For the proverb is true, That light gains make 
heavy purses;' for light gains come thick, whereas 
great gains come but now and then." Bacon. 

(3) "Whatever is given on the evidence of sense may 
be taken as a fact; the existence of God, therefore, 
is not a fact, for it is not evident to sense." 
St. Andrew. 1896. 

(4) "All the trees in the park make a thick shade; this 

is one of them, therefore this tree makes a thick 
shade." Jevons. 

(5) "What we eat grew in the field; loaves of bread are 
what we eat; therefore loaves of bread grew in the 
fields." Jevons. 

(6) "W T ho is most hungry eats most; who eats least is 
most hungry; therefore who eats least eats most." 
Jevons. 

(7) "Great talkers should be cropped, for they have no 
need of ears." Franklin. 

(8) "Love your enemies, for they tell you your faults." 

Franklin. 

(9) "All the works of Shakespeare cannot be read in a 

day; therefore the play of Hamlet, being one of 
the works of Shakespeare, cannot be read in a day." 
Jevons. 

(10) "Logic as it was cultivated by the schoolmen proved 
a fruitless study; therefore logic as it is cultivated 
at the present day must be a fruitless study 
likewise." Jevons. 



Questions for Original Thought 353 

12. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Is there any difference in content between error and 
fallacy? Illustrate. 

(2) In what ways do trusts indulge in sophisms? 

(3) May the sophism be used conscientiously by the country 
doctor ? Explain. 

(4) Give in substance Aristotle's classification of fallacies. 

(5) Select the fallacies which could with justice be called 
fallacies of interpretation. See Creighton. 

(6) Explain in full the popular conception of equivocation. 

(7) Indicate the marks which distinguish the following : 
Ambiguous middle, fallacy of four terms, non sequitur, figure of 
speech. 

(8) "Why should Jeremy Bentham employ a person to read 
to him who habitually read in a monotonous tone of voice?" 
Jevons — Hill. 

(9) Originate a sentence of about ten words and through the 
fallacy of accent secure as many different meanings as possible. 

(10) Show that the fallacy of figure of speech might be 
classed as a fallacy of four terms. 

(11) To what fallacies, in your opinion, are teachers 
especially given? 

(12) Show that the fallacy of accident could be classed as 
one of ambiguous middle. 

(13) "When the Puritan settlers in New England passed 
their three famous resolutions — Resolved, first, that the earth 
is the Lord's and the fullness thereof; secondly, that he hath 
given it to his Saints; thirdly, that we are his Saints. What 
fallacy did the Puritan Fathers commit?" Ryland. 

(14) A Dutchman afflicted with pneumonia arises at midnight 
and eats a large quantity of sauerkraut. The Dutchman gets 
well, whereat his physician writes in his little book on remedies, 
"Sauerkraut sure cure for pneumonia." The physician was guilty 
of what fallacy? Why? 

(15) De Morgan quotes from Boccaccio this: "A servant 
who was roasting a stork for his master was prevailed upon by 
his sweetheart to cut off a leg for her to eat. When the bird 
came upon the table the master desired to know what had 



354 The Logical Fallacies of Deductive Reasoning 

become of the other leg. The man answered that storks never 
had more than one leg. The master, very angry, but determined 
to strike his servant dumb before he punished him, took him 
next day into the fields where they saw storks, standing each 
on one leg, as storks do. The servant turned triumphantly to 
his master; on which the latter shouted, and the birds put down 
their other legs and flew away. Ah, sir, said the servant, you 
did not shout to the stork at dinner yesterday; if you had done 
so he would have shown his other leg." What fallacy does this 
quotation from Boccaccio illustrate? 

(16) Why should begging the question and irrelevant con- 
clusion be classed as fallacies of the "forgotten issue?" 

(17) From the standpoint of both form and meaning test the 
validity of the following: 

(1) "Virtue is the child of knowledge and vice of 

ignorance; therefore education, periodical literature, 
traveling, ventilation, drainage and the arts of life, 
when fully carried out, serve to make a population 
moral and happy." Hibben. 

(2) "The civil power has the right of ecclesiastical 
jurisdiction and administration, therefore parliament 
may impose articles of faith on the church or 
suppress dioceses." Hibben. 

(3) "Seeing that abundance of work is a sure sign of in- 

dustrial prosperity, it follows that fire and hurricane 
benefit industry, because they undoubtedly create \ 
work." St. Andrews — 1895. 

(4) "Riches are for spending, and spending for honor J 
and good action; therefore, extraordinary expense j 
must be limited by the worth of the occasion." 
Bacon. 

(5) "And let a man beware how he keepeth company 

with choleric and quarrelsome persons; for they 
will engage him into their own quarrels." Bacon, i 

(6) "He that resteth upon gains certain, shall hardly grow j 

to great riches; and he that puts all upon adven- I 
tures, doth oftentimes break and come to poverty, i 
It is good, therefore, to guard adventures with 
certainties that they may uphold losses." Bacon. 



CHAPTER 17. 



INDUCTIVE REASONING. 



1. INDUCTIVE AND DEDUCTIVE REASONING DIS- 
TINGUISHED. 

It has been remarked that inference is the process of 
deriving a judgment from one or two antecedent judg- 
ments, and that mediate inference is inference by means 
of a middle term. But to reason by means of a middle 
term necessitates two judgments ; hence mediate inference 
might be defined as the process of deriving a judgment 
from tzvo antecedent judgments. In this treatment 
mediate inference and reasoning have been used inter- 
changeably. This, then, becomes our definition for rea- 
soning: Reasoning is the process of deriving a judgment 
from two antecedent judgments. 

The syllogism results when the process of reasoning 
is formally clothed in words. Moreover, the conclusion 
of the syllogism may be more general than the premises 
or less general. This suggests the two important kinds 
of reasoning; namely, inductive and deductive. Inductive 
reasoning is reasoning from less general premises to a 
more general conclusion. Deductive reasoning is reason- 
ing from more general premises to a less general 
conclusion. 

355 



356 



Inductive Reasoning 



Illustration : 

Inductive Syllogism. 

The robin, crow, sparrow, 

etc. have wings, 
The robin, crow, sparrow, 

etc. are birds, 
.*. All birds have wings. 

Iron, silver, gold, etc. are 

elements, 
Iron, silver, gold, etc. are 

metals, 
.*. All metals are elements. 

Boston, New York, Chicago, 

etc. have fine harbors, 
Boston, New York, Chicago, 

etc. are large cities, 
.". All large cities have fine 

harbors. 

The student who is sufficiently familiar with the canons 
of the deductive syllogism will at once detect the fallacy 
of illicit minor in the foregoing inductive syllogisms; 
i. e., "birds" when used as the predicate of the minor 
premise of the first syllogism is undistributed, but as the 
subject of the conclusion "birds" is distributed. The 
same might be said concerning the terms "metals" and 
"large cities." A portion of this chapter will be devoted 
to answering this criticism. At this point it may be 
stated that the inductive syllogism is not supposed to 
conform perfectly to the canons of the deductive 
syllogism. 

2. THE INDUCTIVE HAZARD. 

Referring to the first inductive syllogism of section 



Deductive Syllogism. 
All birds have wings, 

The robin, crow, sparrow, 

etc. are birds, 
The robin, crow, sparrow, 

etc. have wings. 
All metals are elements, 
Iron, silver, gold, etc. are 

metals, 
Iron, silver, gold, etc. are 

elements. 

All large cities have fine 

harbors, 
Boston, New York, Chicago, 

etc. are large cities, 
Boston, New York, Chicago, 

etc. have fine harbors. 



The Inductive Hazard 357 

one, it is assumed that the robin, crow and sparrow are 
representative birds, and that we are thus justified in 
concluding that if these type birds have wings, then all 
birds must have wings. Of course this is more or less 
of a conjecture or "a hazard"; since birds without wings 
may exist in some undiscovered corner of the globe. 
However, inasmuch as the generalization concerns a rep- 
resentative quality, we deem the assumption fairly well 
founded. The logical right to take this "leap into the 
unknown" will be discussed later. It will profit us at 
this time to realize more fully how essential the "inductive 
hazard" is to the progress of the world. When the 
Schoolmen of mediaeval time refused to venture, they 
failed to progress, and thus came the dark days. When- 
ever man has ignored this God given instinct which leads 
to discovery, the world has stood still. This zvillingness 
to (( take a leap into the dark" with the hope of finding, 
in the shadow, truth which would enhance man's power 
and increase his serviceableness, has given to the world 
about all that is worth while. It was the spirit of the 
hazard which pushed Columbus to the discovery of a new 
world; which gave Newton the secrets of the motions 
of the universe; which enabled Edison to harness a 
multitude of lurking forces; and Morse and Bell to re- 
duce distance to its lowest terms. In ordinary affairs 
with ordinary men those succeed best who manifest most 
a safe, steady, persistent spirit of discovery. Here, then, 
in the "inductive hazard" have we a most important phase 
of school life which, in this day of making the work 
easy, is being sadly neglected. On the other hand, an 



358 Inductive Reasoning 

unregulated and insane spirit of venture may result in a 
great waste of energy, and in the development of low 
ideals of recklessness and inaccuracy. The "inductive 
hazard" must be cultivated; yet it must be regulated as 
well, and, as the reader already realizes, logic needs to 
concern itself mainly with this regulative aspect. 

3. THE COMPLEXITY OF THE PROBLEM OF INDUCTION. 

The problem of induction is much more complex than 
that of deduction because of these reasons: First. De- 
duction as a process of reasoning was the only kind dis- 
cussed by the logicians for two thousand years. Aristotle 
is called the father of deductive logic and this Intellectual 
Giant, the greatest of ancient time and possibly of all 
time, so perfected the form of deductive reasoning that, 
up to the time of Francis Bacon, no scholar possessed 
the temerity to gainsay its supremacy in the field of 
logical reasoning. For twenty centuries Aristotle's De- 
ductive Logic was the Logicians' Bible. On the other 
hand, inductive reasoning, though it was briefly dis- 
cussed by Aristotle, received little attention till the versa- 
tile Francis Bacon placed it upon the stage of the think- 
ing world. This makes deduction nearly two thousand 
years older than induction. Time, by eliminating the 
personal equation and exposing in various ways fallacious 
thinking, tends to unify and universalize truth. Hence, 
logicians are agreed so far as the fundamentals of de- 
ductive logic are concerned, but are still at odds over 
the true conception and use of inductive logic. 

A second reason for this confused status in the field 



The Complexity of the Problem of Induction 359 

of inductive logic is the fact of its being more closely 
related to the events of every day living. Induction is 
the natural method of childhood; the popular method of 
the school room; and the most used method of common 
life. In consequence its ramifications are so varied and 
multitudinous, that it will take centuries of thinking to 
reduce the doctrine of induction to that uniformity and 
defmiteness which so distinguishes deduction. 

4. THE VARIOUS CONCEPTIONS OF INDUCTION. 

The attending quotations will give the student a fair 
idea of the leading conceptions concerning induction: 

(1) "Induction is the process by which we conclude 
that what is true of certain individuals of a class is true 
of the whole class, or that what is true at certain times 
will be true under similar circumstances at all times." 
"Induction, as above defined, is a process of inference ; it 
proceeds from the known to the unknown." "Any 
process in which what seems the conclusion is no wider 
than the premises from which it is drawn, does not fall 
within the meaning of the term." — J. S. Mill, A System 
of Logic, 1892, p. 175. 

(2) "An induction is a generalization or an inference 
based upon propositions that state observed facts." "The 
truth inferred may be general or particular, but it must 
be one which we cannot perceive in a single act of 
observation." — Ballentine's Inductive Logic, 1896, p. 14. 

(3) "Induction is the process of inference by which 
we get at general truths from particular facts or cases." — 
Ryland's Logic, 1900, p. 148. 



360 Inductive Reasoning 

(4) "Induction may be defined as the legitimate in- 
ference of the general from the particular, or, of the 
more general from the less general." — Fowler, 1905, 
p. 10, Vol. 2. 

(5) "The term induction has been used by logicians 
to denote this leap of the mind from the limitations of its 
positive knowledge to belief in universal laws." "In 
pedagogy, however, the term is applied to the whole 
process of arriving at general truths or principles." — 
Salisbury's Theory of Teaching, p. 156. 

5. INDUCTION AND DEDUCTION CONTIGUOUS PRO- 
CESSES. 

If there is one thing above another which modern logic 
is emphasizing it is the unity of the mind and the con- 
tiguity of thinking. Induction and deduction are dove- 
tailed processes which characterize all thinking worthy of 
the name. Where induction ceases, deduction commences, 
and vice versa. It becomes the function of inductive 
thinking to establish a connection between what has been 
experienced and what has not been experienced. There- 
fore, the conclusion of an induction must always contain 
more than is implied in the premises. The premises de- 
note facts which have been observed; whereas the con- 
clusion denotes the observed facts of the premises plus 
analogous facts which have not been observed. Inductive 
thought ventures into the unknown, and attempts to estab- 
lish a bond of connection between it and something 
already known. Induction seeks new knowledge, and 
does so by taking that "leap into the dark" already 
referred to as the "inductive hazard." 



Induction and Deduction 361 

As soon as the mind reaches a universal truth, it sets 
to work to clarify this truth. Such is accomplished by 
reference to other facts which the universal is supposed 
to include ; and this application of the general to the par- 
ticular is deduction. Induction discovers the new knowl- 
edge while deduction clarifies it. 

6. INDUCTION AN ASSUMPTION. 

In this treatment induction as a general process has 
been subdivided into induction as a mode of inference 
and induction as a method. Induction as a mode of in- 
ference is the process of reasoning from less general 
premises to a more general conclusion; zvhereas induction 
as a method is a procedure from the observation of indi- 
vidual facts to a realisation of a universal truth. In 
either case the conclusion of an inductive process always 
implies more than is contained in the premises. This 
gives to the conclusion an uncertainty. No induction is 
absolutely free from doubt except the so-called perfect 
induction, which form will receive attention in a later 
section. 

7. Universal Causation. 

All inductive assumptions are made possible because of two 
laws — universal causation and uniformity of nature. 

The law of universal causation may be stated in this wise : 
Nothing can occur without a cause and every cause has its effect. 
"It is a universal truth, that every fact which has a beginning 
has a cause." — Mill. 

Simple Illustrations of Universal Causation. 
The sun rises in the east. The boy throws a stone through the 



362 Inductive Reasoning 

window. A democratic wave sweeps the country. Prices of food 
stuff are high. The bullet, shot out into space, finally falls to the 
earth. Each one of these occurrences has a cause.* 

That universal causation is a fundamental condition of all 
induction may be further illustrated. The astronomer notes that 
the stars in the vicinity of Vega seem to be moving outward 
from a common center; whereas in the opposite part of the sky 
the stars seem to be moving inward toward a common center. 
Having observed this phenomenon, the astronomer at once looks 
for a cause. Finally he decides that the phenomenon is due to the 
fact that the sun, with his attending family, is moving towards 
Vega. Arranged, the argument may take this form : 

The stars in the vicinity of Vega seem to be moving outward 
from a common center, whereas in the opposite part of the sky 
the stars seem to be moving inward, When descending a moun- 
tain the trees at the foot seem to move outward from, and those 
at the top inward toward, a common center, When riding on the 
train the ties in front seem to move outward while those in the 
rear seem to move inward. From this we conclude that the sun 
with the Earth and other planets is moving toward a spot in the 
sky near Vega. Were it not for the assumption that the 
phenomenon relative to the stars had a cause there could have 
been no induction. Moreover, any investigation concerning "dem- 
ocratic waves," "prices of food stuffs," etc., must assume as a 
starting point that these phenomena have causes. 

It would appear that the mind is not satisfied with a mere 
passive observation of the occurrences of the world but is in- 
clined to reach out for the "whys and wherefores." Due partly 
to this reason, '"universal causation" is often referred to as an 
a priori law; meaning that it is a law which cannot be proved, 
but must be assumed in all thinking. 

8. The Law of the Uniformity of Nature. 

Law stated : The same antecedents are invariably followed by 
the same consequents. "That the course of nature is uniform is 



* This cause, however, need not be a single antecedent, in fact it 
seldom is. "This cause, philosophically speaking, is the sum total of 
the conditions, positive and negative, taken together." — Mill. The 
cause of the price of food stuff being high, involves many condi- 
tions, or antecedents, so interwoven that it is impossible to designate 
any one as being the chief factor concerned. 



Induction an Assumption 363 

the fundamental principle of induction." — Mill. "It is not 
enough to feel assured that nothing can happen without a cause 
(causation) ; I must also feel assured that the same cause will 
invariably be followed by the same effect." — Fowler. 

Referring to the observed phenomenon of the outward move- 
ment of the stars about Vega, the astronomer might advance as 
an hypothesis the fact of the solar system's movement toward 
Vega. Having done this he could then experiment with a view 
of verifying this hypothesis. In this experiment he would 
attempt to introduce the same cause surrounded by similar cir- 
cumstances, and then watch for the same effect. To make it 
concrete : suppose the astronomer paints the side of a barn 
dark blue and bedecks this with stars of white. Then taking a 
position as far removed from the blue surface as his eyesight 
will permit, he runs toward the barn watching the apparent 
movement of the artificial stars. A similar experiment could be 
performed by substituting for the starred barn, the stumps on a 
side hill. In both experiments he assumes that like conditions 
will be followed by constant results. That is, in these particular 
cases, advancing toward a group of objects is always followed by 
an apparent separation of said objects. 

This law of uniformity of nature not only underlies inductive 
thinking but it really conditions all thinking. It implies that the 
universe is a rational system functioning in a uniform manner. 
Moreover, it suggests that the interpretations of the mind are 
likewise uniform and whenever the mind proves a fact to be a 
universal truth, this truth will always remain a truth unless the 
conditions change. In fact were it not for the uniformity of 
nature, all activity whatsoever would be rendered nugatory. 
Because of this law we have a right to assume that grinding a 
knife under right conditions will always tend to sharpen it; that 
surrounding a live seed with a proper environment will result in 
growth; that water at the same altitude will boil at a constant 
temperature, etc., etc. 

The student will discern the close connection between these 
two laws and the laws of thought. There is really no distinctive 
mark between the law of causation and the law of sufficient 
reason, while "uniformity of nature" includes identity as one of 
its distinctive features. The laws differ, however, in their appli- 



364 Inductive Reasoning 

cation, "causation" and "uniformity of nature" conditioning 
inductive thinking, while the others are concerned with deductive 
thinking. 

Because "uniformity of nature" expresses facts of experience, 
it is regarded as an empirical law, as contrasted with the law of 
causation, which is supposed to be based upon an innate mental 
conception or is an a priori law. 

9. INDUCTIVE ASSUMPTION JUSTIFIED. 

The function of induction seems to be to universalize 
particulars. The mind of man has ever been engaged in 
establishing connections among the concrete experiences 
of daily life. This ability of his to generalize his indi- 
vidual experiences has been one of the chief agencies in 
elevating him to the position of "King of the animal 
world." In this disposition to generalize man has taken 
it for granted that nature is honest; that what she tells 
him under given conditions, she will tell him again under 
identical conditions. To put it in logical terms man can 
depend upon the invariability of nature's activities, or 
upon the uniformity of nature. Here, then, is one of the 
most fundamental laws not only of induction but of all 
activity. But this law implies a second quite as funda- 
mental. If every cause is invariably followed by the same 
effect under like conditions, then it is thereby implied 
that every cause has an affect and every event is due to 
some cause. This, too, is invariable. In consequence of 
these facts man is justified in thinking that nature is not 
only honest and therefore "she gives me confidence, but 
her every activity means something and therefore she 
arouses my curiosity." ''Uniformity of nature'' engenders 
confidence, "universal causation" inspires the spirit of dis- 



Inductive Assumption Justified 365 

covery and with these two weapons man is willing to 
venture into the jungle of the unknown. Why is man 
eager to undertake the "inductive hazard?" Because, 
through the laws of universal causation and uniformity 
of nature, his curiosity is aroused, and he is given confi- 
dence in nature's activities. 

10. THREE FORMS OF INDUCTIVE RESEARCH. 

Induction is a matter of universalizing less universal 
experiences. In this the process may assume any one of 
three forms, namely : ( 1 ) Induction by simple enumera- 
tion; {inductio per enumerationem) : (2) Induction by 
analogy; (3) Induction by analysis. 
Three Forms Illustrated: 

(1) Simple enumeration. 

Having observed a few instances the generalization is, 
"All birds have wings." The certitude of this may now 
be strengthened by observing more birds and finding 
without exception that each has wings. 

(2) Analogy. 

By noting on Mars geometric markings which resemble 
canals, the generalization is vouchsafed that Mars is 
inhabited by human beings. Other similarities in atmos- 
pheric conditions, existence of land and water, etc., tend 
to make this generalization more plausible. 

(3) Analysis. 

By analyzing water taken from a certain spring, it is 
found to contain hydrogen and oxygen in the proportion 
of 1 to 8 ; in consequence a generalization to this effect is 
posited. Analyses of specimens from other sources yield 



366 Inductive Reasoning 

similar results and thus the generalization is given greater 
certitude. 

As a usual thing the particular form which the induc- 
tion assumes depends on the nature of the topic under 
investigation and also on the mental make-up of the 
investigator. The general statement that all birds have 
wings could hardly be derived by means of analogy or 
analysis, but is a matter of a casual observation of many 
instances. Moreover, that mind given to accurate ob- 
servation, but not inclined to note resemblances or to 
carry on experiments, would naturally follow the first 
inductive type. On the other hand, simple enumeration 
would be impossible in questions like the habitability 
of Mars, and would yield no results in cases requiring 
definite scientific experimentation like electrolysis. 

It is worthy of note that some topics lend themselves to 
all three modes of procedure. To wit : ( 1 ) Enumeration. 
Without being taught the rule the child is given a list of 
examples involving the dividing of a decimal by a decimal 
and is asked to solve them. By comparing his answers 
with those in the book, he somewhat accidentally dis- 
covers what seems to be the correct rule for pointing off 
in the quotient. By following this rule and each time com- 
paring answers he establishes the truth. (2) Analogy. If 
.24 -j- .6 is the first example, the child may resort to the 
weil known process of dividing a common fraction by a 



common fraction 



(24 60 24 4 \ 
: = — = — , 1 then, because 
100 roo 60 10 / 
of their close resemblance, he may reason that decimal 

fractions should yield the same result. (3) Analysis. 



Inductive Assumption Justified 367 

Here the child reasons that since division of decimals is 
the inverse of multiplication of decimals, the rule for 
pointing off might be the inverse of the multiplication 
rule. By trying this out and proving his answer in each 
example, he becomes convinced of the correctness of his 
reasoning. 

11. INDUCTION BY SIMPLE ENUMERATION. 

As its name implies this type of inductive research 
consists in observing many instances which may exemplify 
the particular uniformity under consideration. The 
process is quantitative rather than qualitative, the certi- 
tude of the generalization depending on the mass of facts 
collected rather than on any striking resemblance or any 
detailed analysis. The aim is to observe, accurately if 
not scientifically, instance after instance until all doubt 
is removed. The outcome of such observation may be 
three fold. (1) The enumeration may be complete. 
This gives the so-called "perfect induction" which will 
receive attention later. (2) The enumeration may be in- 
complete and without exceptions; generalizing in this 
way from uncontradicted experience gives what are 
termed c< empiric aY' truths. (3) The enumeration may 
be incomplete with exceptions. It is obvious that this 
type of induction could give no valid generalization; but 
the result may be put in the form of a ratio between the 
uniformities and the exceptions. Such a procedure is a 
mere ce calculation of chances' and the result simply an 
expressed probability. 



368 Inductive Reasoning 

The Three Kinds of Simple Enumeration Illus- 
trated . 
The subject to receive investigation is a school exami- 
nation. 

(1) Complete enumeration. Every paper is read 
and marked; this leads to the generalization, "All the 
class have passed." 

(2) Incomplete enumeration with no exceptions. 
Representative papers are read and marked in which no 
failures are found. Generalization, "Probably all of the 
class have passed." 

(3) Incomplete enumeration with exceptions. Rep- 
resentative papers are read and marked in which there 
are 20 failures out of the hundred papers examined. 
Generalization, "Probably about 80% of the class have 
passed." 

Briefly, simple enumeration may take the form of (1) 
a perfect induction, (2) a probable induction, (3) a mere 
calculation of chances. The first necessitates completed 
experience, the second uncontradicted experience and 
the third contradicted experience. 

12. INDUCTION BY ANALOGY. 

Induction by analogy assumes that if two {or more) 
things resemble each other in certain respects, they belong 
to the same type, and, therefore, any fact known of the 
one may be affirmed of the other. 

The Type. 

As the definition implies, analogy involves an extensive 



Induction by Analogy 369 

use of types; let us, therefore, become better acquainted 
with them as instruments in analogical inductions. A 
type is one of a group which embodies the essential char- 
acteristics of that group. How easy and natural it is to 
dismiss a complex topic with the citing of an example 
which may be regarded as a type; how common is the 
use of examples in the school room ! On second thought 
it becomes apparent that analogical induction by example 
or type is the most common of all forms of induction 
either as a method or a mode of inference. Analogy by 
example {or type) assumes that if two or more things 
are of the same type, they resemble each other in every 
essential property. 

Illustrations of analogical inductions by example or 
type. 

(1) Mathematics. 

Example: a + b 
a + b 



l 2 + ab 
+ ab + 



a 2 + 2 ab + b 2 

Inductive Inference: The square of the sum of two 
quantities is equal to the square of the first, plus twice 
the first by the second, plus the square of the second. 

(2) Nature. 

This corn sent me as a sample produced heavy, full 
ears, and many of them; hence (inductive inference), if I 
plant corn like this sample under like conditions, I will 
receive in return heavy, full ears, and many of them. 



370 Inductive Reasoning 

(3) Geography. 

Cities like New York, located on the coast, possess 
a larger foreign element than the inland cities like 
Philadelphia. 

(4) Grammar. 

A noun is the name of anything, as the examples, 
"George Washington" and "house" would indicate. 

In deriving a generalization from one or two examples 
the prime essential is to select types which are truly 
representative. Often the example used is a special type 
and in consequence does not exemplify all of the essen- 
tial characteristics of the group. To teach the nature of 
a parallelogram by using a rectangle only, is an easy way 
to commit this error ; or one may affirm that the class can 
easily cover the work, when the judgment is based en- 
tirely on knowledge concerning the brightest one of the 
grade. 

Type work when judicially used is a positive time saver 
and a very present help in times of perplexity. Let the 
skillful teacher use types and examples extensively yet 
cautiously. 

The Mark of Similarity. 

As opposed to analogy by type there is a second form ; 
namely, analogy by one or more similar marks or quali- 
ties. This form is best described by the definition : 
When two things resemble each other in a few marks or 
qualities they resemble each other in other marks or 
qualities. 



Induction by Analogy 371 

Illustrations of analogy by marks. 

(1) Noting that two students have the same sir- 

name, I infer that they are brothers. 

(2) A man with a book under his arm rings the 

door bell and asks to see "the lady of the 
house." At once the conclusion is drawn that 
the caller is a book agent. 

(3) Two automobiles, resembling each other in shape 

of body, force one to the conclusion that the 
machines are of the same make. 

The Errors of Analogy by Marks of Similarity. 

It follows that analogy by example gives generalizations 
of much greater certitude than analogy by one or two 
marks of resemblance. Here is a field bespattered from 
boundary to boundary with erroneous thinking. The 
principle of resemblance being an innate tendency, this 
form of error is most common with the immature. The 
child reasons by analogy when he invests the poodle with 
the despised cognomen of "kitty" ; or honors every man 
who wears glasses with "papa." In 'the childhood of the 
race natural events were interpreted by means of 
analogy. The wind blowing through the trees made 
sounds much like the human voice; hence these noises 
were attributed to spirits. Primeval man was led to 
believe by analogy that everything which moved was 
alive. We may, therefore, think of our revered forbear as 
engaged in the undignified task of running after his 
shadow, or chasing a leaf around a stump. 



372 Inductive Reasoning 

The Value of Analogy. 

Analogy being rich in its suggestions is the favored 
process of the scientist and inventor. Newton reasoned 
by analogy when he tentatively affirmed of the moon 
what he positively knew of the apple. Franklin's reason- 
ing was analogical when he discovered the identity of the 
electric spark and lightning. Because this form of induc- 
tion so often leads to error and at best involves a degree 
of probability far below induction by analysis, some logi- 
cians are inclined to ignore its generalizations altogether. 
Others deem this a mistake because of these reasons: 
First. Analogy is serviceable to a high degree in sug- 
gesting hypotheses which may be advanced either for the 
purpose of explanation or verification. It has already 
been indicated that analogy is the common instrument 
used by the inventor and discoverer. Second. The prin- 
ciple of analogy, in reality, lies at the basis of classifica- 
tion; because in this, things are grouped according to 
their resemblances. Third. Analogical induction affords 
valuable training in originality and initiative. A mind 
which easily and naturally discerns analogies is "fertile in 
new ideas." 

Requirements of a True Analogy. 

It has been remarked that the certitude of an induction 
by simple enumeration depends upon the number of un- 
contradicted instances. In analogy the case is different 
as the process emphasizes the weight of the points of 
resemblance rather than the number. In substance the 
requirements of a logical analogy are three. 



Induction by Analogy 373 

First. The points of resemblance must be representative 
and not exceptional. For example: The argument that 
Mars is inhabited because it has two moons is of little 
worth, since we have no proof that moonshine is essential 
to life; this point of resemblance is not representative. 
On the other hand, if the basis of argument is the fact 
that Mars has an atmosphere, the conclusion carries some 
weight; as air seems to be essential to life. 

Second. The points of resemblance must outweigh 
the points of difference. That is, the ratio of probability- 
must always be in favor of the resembling instances. 
Since it is not a matter of numbers but of weight, a 
numerical proportion like this would he misleading: 
Resemblances: Differences = 10: 6. It is obvious that 
the six differences might more than outweigh the ten re- 
semblances. The safer way, if it were possible, would be 
to attach a value to each point of resemblance or differ- 
ence, and then express the proportion in terms of the 
sums of these values. 

Third. There must be no difference which is abso- 
lutely incompatible with the affirmation which we wish to 
prove. For example, the fact that the moon has no 
atmosphere renders nugatory any attempt to prove the 
habitability of the moon. 

13. INDUCTION BY ANALYSIS. 

This, the third form of inductive research, is by far 
the most important. Simple enumeration, because it de- 
pends upon the number of observed instances, consumes 
much time; while we have already noted how easy it is 



374 Inductive Reasoning 

for analogy to lead to error. At the best, the conclusion 
of these methods must be subjected to analytic investiga- 
tion, if we are seeking universal validity. Induction by 
analysis is superior to the other forms because it secures 
a higher degree of probability and is a positive time saver. 
Defined. We have learned that analysis is the process 
of separating a whole into its related parts. We thus 
define induction by analysis as the process of separating a 
whole into its parts with a view of deriving a generalisa- 
tion relative to the nature and causal connection of these 
parts. 

Illustrations : 

( i ) Concerning the generalization that "all birds have 
wings," it becomes possible to observe in detail the nature 
of the wings and advance the hypothesis that these wings 
are designed for aerial navigation. This hypothesis may 
then be strengthened by observing that the entire struc- 
ture of the bird is adapted to flying. 

(2) If it were possible to analyze the atmosphere, 
water, and soil of Mars, and should such analysis reveal a 
composition similar to that of the earth, it would illustrate 
well not only the method of analysis but also its superiority 
over the other methods of investigation. 

(3) The physician, in diagnosing a "case," observes 
that the symptoms resemble those of typhoid; but to be 
positive of the truth of his diagnosis, he takes a blood 
test. Noting the resemblances is induction by analogy; 
but the blood test involves induction by analysis. 

Induction by analysis concerns hypothesis, observation, 



Induction by Analogy 375 

and experiment, including Mill's experimental methods. 
These topics will receive due attention in the chapters 
which follow. It will be sufficient to close this discussion 
with a brief treatment of perfect induction, and traduction. 

14. PERFECT INDUCTION. 

As has been indicated under simple enumeration, a 
perfect induction is one in which the premises enumerate 
all the instances denoted by the conclusion. 
Illustrations : 

(1) A, B, C, D, and E are all Reactionaries, 

(All) The members of the committee are A, B, 
C, D, and E, 
.'. (All) The members of the committee are Re- 
actionaries. 

(2) John, James, Albert, and Peter all have perfect 

eyesight, 
John, James, Albert, and Peter are all rthe 
boys of my family, 
.'. All the boys of my family have perfect eyesight. 

(3) The first, second, and third groups are up to 

grade, 
The first, second, and third groups include all of 

the children in my room, 
Hence all the children in my room are up to 

grade. 

Because the conclusion of a perfect induction gives 
nothing new — nothing but what is found in the premises, 
some claim that the process is practically valueless. From 



376 Inductive Reasoning 

the viewpoint of the discoverer this position is well taken; 
yet to universalize particular observations puts the knowl- 
edge in compact, usable form, and saves one the trouble 
of returning each time to the consideration of each par- 
ticular. Thus as a process which leads to verified uni- 
versal, perfect induction is a time saver. In the second 
place it was the method used by Socrates when he desired 
to lead up to a definition or some other general truth. 
The Sophists were given to a careless use of the "in- 
ductive hazard" ; they were prone to generalize from one 
or two particulars, or what is worse, to establish a gen- 
eralization and then attempt to fit the particular instances 
to it. This led to a superficiality which the Great Pagan 
Educator abhorred. The fact that perfect induction was 
the method used by Socrates to counteract the teachings 
of the Sophists, is sufficient vindication for its use in 
discouraging the indefensible assumptions of to-day, and 
in inspiring warrantable generalizations based on accurate 
observation. 

In the school room with classes addicted to careless, 
inaccurate work, to accept nothing but a perfectly induced 
generalziation, when this is feasible, is a most valuable 
lesson. For example, the teacher may not accept the 
generalization that all of the "first class" cities of the 
U. S. are located on navigable waterways, until the pupils 
have investigated the waterway conditions of every city 
belonging to the class. On the other hand, there may be 
individual cases of "cocksureness" which need attention. 
The teacher can do little for the "know-it-all youngster" 
until he pricks the bubble of conceit. This may be accom- 



Perfect Induction 377 

plished by allowing the youth to draw a generalization, 
which seems to meet all the requirements of truth arrived 
at by means of an imperfect induction; then without 
warning let the teacher give an instance which will show 
the generalization to be false. This involves what 
Socrates termed the "torpedo's shock." To illustrate: 
Consider the "prime number" formula given by Jevons. 
In deriving this, direct the class to add 2 to its square, 
and to this sum add 41. Give similar directions relative 
to numbers 3, 4, 7 and 10. Indicating the work as 
directed, would give the following: 

(1) 2+ 2 2 + 4i= 47 

(2) 3+ 3 2 + 4i= 53 

(3) 4+ 4 2 + 4i= 61 

(4) 7 + 7 2 + 4i= 97 

(5) IO+I0 2 + 4I=rl5I 

A question or two will make apparent the fact that all 
the results are prime numbers, and then the generalization 
may be drawn ; namely, X + X 2 + A 1 — prime number. 
Now without warning, but under the assumption that you 
desire to test deductively the general formula, let X = 40. 
This gives (40 + 40 2 + 41) 1681, which is the square of 
41 and is, therefore, not a prime number. 

15. TRADUCTION. 

It may have been noted by the student that "perfect 
induction" is not induction at all according to the defini- 
tion ; viz. : Inductive reasoning is reasoning from less 
general premises to a more general conclusion. Referring 
to the first illustration of the previous section it is appar- 



378 Inductive Reasoning 

ent that the conclusion is no broader than the premises. 
Ostensibly, the conclusion is a mere summary, or a 
generalization of the facts mentioned in the premises. 
Moreover perfect induction does not readily conform to 
the definition of deductive reasoning, as in this the move- 
ment must be from the more general to the less. We are 
thus forced to the conclusion that perfect induction is a 
form of a third type of reasoning which is knov/n under 
the cognomen of traduction. This is from the Latin 
trans, and ducere meaning to lead across. Definition: 
Traductive reasoning is reasoning to a conclusion which 
is neither less general nor more general than the premises. 
Aside from the case of perfect induction there are 
other types which well illustrate traduction. These are: 
First. Reasoning from particular {or individuals) to 
particular (or individuals). 

Illustration : 

Highland Street is the longest street in Jamaica, 
Highland Street is not so long as Broadway of 
New York City, 
.'. The longest street of Jamaica is not so long as 
Broadway of New York City. 
Second. Reasoning from general to general. 

Illustration : 

All growing things die, 
All living things are growing things, 
.'. All living things die. 
It may be observed that all of the propositions in traduc- 
tion are co-extensive "A's" or "E's"; hence all the 



Traduction 379 

terms are distributed. This eliminates any possibility of 
committing fallacies of distribution. Further, the propo- 
sitions may be interchanged at will, without invalidating 
the particular conclusion selected. To illustrate we may 
change the last argument to this : 

All growing things are living things, 
All things that die are growing things, 
.'. All things that die are living things. 
From the viewpoint of authenticity traduction is the 
most, and induction the least dependable; whereas the 
certitude of deductive reasoning lies somewhere between 
the two. On the other hand, when looked at from the 
ground of serviceableness the order is reversed, induction 
being the most useful form of inference and traduction 
the least. 

16. OUTLINE. 

Inductive Reasoning. 

(1) Inductive and Deductive Reasoning Distinguished. 

(2) The "Inductive Hazard." 

Essential in world's progress. 
Cultivated and regulated in school. 

(3) Complexity of the Problem of Induction. 

(4) Various Conceptions of Induction. 

Quotations from prominent authorities. 

(5) Induction and Deduction Contiguous Processes. 

(6) Induction an Assumption. 

A mode of inference; A method. 

(7) Universal Causation. 

Law stated and illustrated. 
Conditions all induction. 

(8) Uniformity of Nature. 

Denned and illustrated. 



380 Inductive Reasoning 

Conditions all induction. 
Empirical. 

(9) Inductive Assumptions Justified. 

(10) Three Forms of Inductive Research. 

(1) Enumeration (2) Analogy (3) Analysis. 

Illustrated. 

Conditions determine form followed. 

(11) Induction by Simple Enumeration. 

Defined and illustrated. 

Outcome threefold — these illustrated. 

(12) Induction by Analogy. 

Two conceptions. 

Analogy by type or example. Illustrations represent- 
ative. 
Error of analogy. 
Suggestiveness of analogy. 
Value of analogy. 
Requirements of a true analogy. Three. 

(13) Induction by Analysis. 

Importance. 

Defined and illustrated. 

(14) Perfect Induction. 

Defined and illustrated. 

Its use. 

Method of Socrates. 

(15) Traduction. 

Defined and illustrated. 
Three methods compared. 

17. SUMMARY. 

(1) Reasoning is the process of deriving a judgment from 
two antecedent judgments. The syllogism is a common form of 
expressing the process of reasoning. 

Inductive reasoning is reasoning from less general premises to 
a more general conclusion. 

Deductive reasoning is reasoning from more general premises 
to a less general conclusion. 

The inductive syllogism is not supposed to conform to the 
canons of the deductive syllogism. 






Summary 381 

(2) Positing in the conclusion more than is indicated in the 
premises involves what is known as the "inductive hazard." 

The inductive hazard which is another expression for the 
spirit of discovery, should be fostered in the school room since it 
has been one of the great forces in human progress; but this 
venturesome spirit must be regulated by rules, principles, and 
systematic procedure, or low ideals of recklessness and inaccuracy 
will result. 

(3) The problem of induction is more complex than that of 
deduction; because the former is a comparatively new subject, 
and also is more closely related to the activities of life. 

(4) The opinion relative to the exact nature of induction, 
though varied, may be summed up in the thought of its being 
the process which leads to general truths, derived from the 
observation of individual facts. 

(5) Induction and deduction are contiguous processes which 
go to make up the more general process of thinking. Where 
induction ceases, deduction naturally commences; induction 
discovers new knowledge, deduction clarifies it. 

(6) Induction as a general process may be treated as a mode 
of inference or as a method. In either case the conclusion 
comprehends more than is contained in the premises. 

Since no imperfect induction is absolutely free from doubt, on 
what ground are we justified in making any inductive 
assumptions ? The answer follows : 

(7 and 8) "Nothing can occur without a cause and every 
cause has its effect," is the law of universal causation; while the 
law of the uniformity of nature is "the same antecedents are uni- 
versally followed by the same consequents." These two laws 
justify inductive assumptions, and, in a sense, condition all 
thinking.. 

(9) Uniformity of nature gives man confidence, while uni- 
versal causation arouses his curiosity. With these two weapons 
he is willing to "march into the unknown." 

(10) As the process of universalizing individual experiences, 
induction assumes the three forms of simple enumeration, 
analogy and analysis. The form adopted is not always elective 
but is controlled largely by the exigency of the case. Some 
topics lend themselves to all three modes. 



382 Inductive Reasoning 

(11) Induction by simple enumeration consists in observing 
many instances which exemplify the uniformity under considera- 
tion. Complete enumeration gives the so called perfect induc- 
tive inference; incomplete but uncontradiced enumeration leads 
to empirical truths; while incomplete and contradictive enumera- 
tion involves a mere calculation of chances. 

(12) Induction by analogy assumes that if two (or more) 
things resemble each other in certain respects, they belong to the 
same type, and, therefore, any fact known of the one, may be 
affirmed of the other. 

A most common form of analogy is reasoning by type or 
example. In this it is assumed that if two or more things are 
of the same type, they resemble each in every essential property. 
The type must be truly representative. A second form of 
analogy is reasoning by marks of resemblance. This second form 
often leads to egregious error. 

Analogy is especially valuable in suggesting hypotheses and 
in giving training in originality and initiative. 

A true analogy demands that the points of resemblance be 
representative ; that they outweigh the points of difference, and 
that no disagreement be incompatible. 

(13) Induction by analysis is the process of dividing a whole 
into its parts with a view of deriving a generalization relative 
to the nature and causal connection of these parts. 

Induction by analysis makes use of the hypothesis, of observa- 
tion and experiment, including Mill's five methods. 

(14) A perfect induction is one in which the premises enu- 
merate all of the instances denoted by the conclusion. It is ser- 
viceable in inspiring care and accuracy in the establishment of 
generalizations. 

(15) Traduction is the process of reasoning to a conclusion 
which is neither less general nor more general than the premises. 

Traduction includes reasoning from particular to particular or 
from general to general. Perfect induction is in reality a form 
of traduction. 

Induction, though the most useful form of inference, is the 
most untrustworthy; whereas traduction is just the reverse of 
this. 



Review Questions 383 

18. REVIEW QUESTIONS. 

(1) Define and illustrate reasoning. 

(2) Distinguish by definition and illustration between induc- 
tive and deductive reasoning. 

(3) Explain the "inductive hazard" and show its use to man. 

(4) ''For twenty centuries Aristotle's Deductive Logic was 
the logician's bible." Explain this. 

(5) Show that induction and deduction are contiguous 
processes. 

(6) Distinguish between induction as a mode of inference 
and induction as a method. 

(7) State and explain the law of universal causation. 
Illustrate fully. 

(8) Make evident that a cause may involve many antecedents. 

(9) State and explain by illustration the law of uniformity 
of nature. 

(10) Verify by illustration the notion that the "fact of 
causation" conditions all induction. 

(11) Which of the two laws is empirical, "causation" or 
"uniformity"? Why? 

(12) ShoW that induction is a form of thinking. 

(13) Why should the law of uniformity of nature convince 
man that nature is honest? Illustrate. 

(14) Show that the law of universal causation stirs the spirit 
of discovery. 

(15) Name and illustrate the three forms of induction. 

(16) Why is it that the tendencies of the investigator often 
determine the inductive form which he adopts? 

(17) Explain by illustration the three-fold outcome of 
induction by simple enumeration. 

(18) Selecting some class room experience, illustrate analogy 
by example or type. 

(19) Define and exemplify types as used in logic. 

(20) Remark upon the errors incident to analogy. 



384 Inductive Reasoning 

(21) Summarize the advantages which induction by analogy 
offers. 

(22) State and exemplify the requirements of true analogies. 

(23) Indicate the superiority of induction by analysis over 
the other two forms. Illustrate. 

(24) Define and illustrate perfect induction. 

(25) Under what circumstances is perfect induction justified? 

(26) Define and illustrate traduction. 

(27) Indicate the various forms of traduction. 

19. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Show the connection between illicit minor and the "in- 
ductive hazard." 

(2) Show by illustration that time tends to universalizie 
truth. 

(3) "Induction and not deduction is the natural method of 
the child mind." Prove the correctness of this statement. 

(4) "Induction is the process of inference by which we get at 
general truths from particular facts or cases." Prove that this 
is not strictly correct according to definition. 

(5) As related to establishing general truths, what are the 
special functions of induction and deduction? 

(6) Show that an inductive inference must of necessity be 
more or less uncertain. 

(7) Is there any distinction between the laws of universal 
causation and sufficient reason? Hyslop's Elements of Logic, 
page 329. 

(8) Show that universal causation and uniformity of nature 
are complementary laws. Hyslop, p. 330. 

(9) Relate the "fact of causation" to the laws of thought. 

(10) Distinguish between empirical and "a priori" laws. 

(11) When Harvey discovered the circulation of the blood, 
what form of induction did he use? 

(12) What form of reasoning did Columbus follow in proving 
that the earth is spherical? 



Questions for Original Thought 385 

(13) "It is said that the greatness of Darwin was due 
largely to his habit of never ignoring an exception." Justify by 
illustration the truth of this assertion. 

(14) In analogical reasoning by example, under what 
conditions would one illustration be as convincing as many? 

(15) "Considering the similarities and differences, the weight 
of the argument favors Mars' habitability." Suppose the propor- 
tion of probability were something like this — Resemblances: 
Differences=8 :7; wherein might the conclusion be erroneous? 

(16) Mention a mark or characteristic which would make 
the habitability of Mars incompatible? 

(17) Select a topic for investigation which is peculiarly 
adapted to enumeration; to analogy; to analysis. 

(18) "The uniformities we expect to find in the world take 
two main aspects, one of which is indicated by the term thing 
and the other by the term circumstance" Aikin's Principles of 
Logic, 1905; p. 233 In the light of the two fundamental laws 
of universal causation and uniformity of nature explain and illus- 
trate the quotation. 

(19) Explain the principle of teleology as related to analogy. 
Hibben, 1908; p. 317. 



CHAPTER 18. 

THE FIVE SPECIAL METHODS OF OBSERVATION AND 
EXPERIMENT.* 

1. THE AIM OF THE FIVE METHODS. 

The primary forms of induction have been divided into 
simple enumeration, analogy and analysis. Conditioning 
these forms are the two laws, uniformity of nature and 
universal causation. Since these laws are always con- 
cerned with causes, we may refer to them as together 
expressing the fundamental ''fact of causation." Wherever 
there is a causal connection, no matter how slight, these 
laws obtain. 

Though "the fact of causation" probably conditions all 
forms of induction, it is most conspicuous in the third 
form ; namely, Analysis. Here the main aim is to estab- 
lish a causal connection of some kind ; an aim which may 
be accomplished through the medium of observation and 
experiment. Incident to this notion, John Stewart Mill 
formulated five experimental methods of induction. 
These are known according to the following distinctive 
titles : 

i. The Method of Agreement. 

2. The Method of Difference. 

3. The Joint Method of Agreement and Difference. 

4. The Method of Concomitant Variations. 

5. The Method of Residues. 



* Those might be named the Five Special Methods of Induction 
by Analysis. 



Method of Agreement 387 

2. METHOD OF AGREEMENT. 

(1) Principle stated. As stated by Mill the principle 
of the Method of Agreement is this: "If two or more 
instances of the phenomenon under investigation have 
only one circumstance in common, the circumstances in 
which alone all the instances agree is the cause (or effect) 
of the given phenomenon." 

This notion is given in clearer terms by Jevons and 
Creighton. Viz. : "The sole invariable antecedent of a 
phenomenon is probably its cause" ; and "The sole in- 
variable consequent of a phenomenon is probably its 
effect:' 

It is known that an antecedent is anything which pre- 
cedes; while a consequent is anything which follozvs. To 
be regarded as a cause, an antecedent must be invariable, 
and to be regarded as an effect, a consequent must like- 
wise be invariable. Antecedents and consequents which 
are in no way constant could hardly have any causal 
connection. 

(2) Method symbolized. Let P l5 P 2 , P s , P 4 , etc., 
represent the phenomenon as it may appear the first, 
second, third, fourth, etc., times, and let A, B, C, etc., 
stand for the various antecedents, or the various conse- 
quents as the case may demand. These two forms may 
now be used to illustrate the two statements which 
summarize Agreement: 

First statement. 

Antecedents. Consequents. 

ABC D P t 

A D E F P 2 



388 Methods of Observation and Experiment 

A L M N P 3 

A O P Q P 4 

Second statement. 

P x A BCD 

P 2 A D E F 

P 3 A L M N 

P 4 A O P Q 

In the first case, the sole invariable antecedent is A, 
and, therefore, we infer that A is probably the cause of P. 
In the second case, the invariable consequent being A, is 
probably the effect of P. 

(3) Concrete examples illustrating first statement. 
The Problem: Cause of John's tardiness. 
On investigation the various antecedents are these: 
(1) John has his breakfast at seven; (2) after breakfast 
he carries his father's dinner to him and (3) feeds the 
hens ; and then (4) goes to school by the path through the 
woods and around the mill pond. 

Phenomenon as a consequent. John is tardy. 
Determining to do away with the tardiness, the teacher 
brings about a variation in the antecedents, varying one 
at a time taken in the order indicated above. 
To wit : ( 1 ) Varying the first antecedent. 
John breakfasts at 6:30; 
Other antecedents the same; 
(Phenomenon) But John is tardy. 

(2) Varying the second antecedent. 

The younger brother carries the dinner ; 
Other antecedents the same ; 
(Phenomenon) John is tardy. 



Method of Agreement 389 

(3) Varying the third antecedent. 

Another brother cares for the hens ; 
Other antecedents the same ; 
{Phenomenon) John is still tardy. 

The teacher is now quite certain that the tardiness is due 
to the route through the woods and around the pond. 

Using, as symbols, the initial letters of the italicized 
"key-words" of the antecedents as stated above, the case 
of tardiness may be symbolized as follows : 

Key words Symbols 
seven s 

dinner d 

hens h 

woods w 

tardy t l> t 2 , t 3 

Antecedents Phenomenon 

s d h w t x 

e d h w 1 2 

s b h w 1 3 

s d a w 1 4 

V standing for route through the woods, is seen to be 
the invariable antecedent. 

(4) Concrete example illustrating the second state- 
ment. 

The Problem: To determine the effect of direct 
primaries. 



390 Methods of Observation and Experiment 



First trial. 

Antecedent 

Direct primary 

Second trial. 

Direct primary « 



Third trial. 



Direct primary 



Consequents 
i. Greater expense to candidate, 

2. Greater interest shown, 

3. Better men nominated, 

4. "Bumper" crops. 

1. Greater expense to candidate, 

2. Greater interest shown, 

3. Better men nominated, 

4. Crops below average. 

1. No greater expense, 

2. Greater interest shown, 

3. Better men nominated, 

4. Crops average. 



Fourth trial. 



Direct primary 



1. No greater expense, 

2. No greater interest, 

3. Better men nominated, 

4. Crops average. 

It is seen that the invariable consequent is, "Better men 
nominated." We may, therefore, conclude that this is a 
probable effect of "Direct primaries." 

(5) Distinguishing features of method of agreement. 
The essential characteristics of the method of agree- 
ment are three: 

First, The phenomenon always occurs. 

Second, There is at least one invariable antecedent. 

Third, The other antecedents vary. 



i 



Method of Agreement 391 

Giving attention to the attending symbolized illustrations 
it may be noted that "P," the phenomenon, always hap- 
pens ; while in the case of the first symbolization, "D" is 
the invariable antecedent and "A, B, C, E, G, L, M, F, I" 
are the variable antecedents. "K" is the invariable ante- 
cedent of the second and "H, I, L, T, M, W, X, Y, Z, S" 
are the variable antecedents. 

Antecedents Consequents 

1. A B C D E V x 

A B C D G P 2 

L B C D M P 3 

A F G D M P 4 

L B C D I P 5 



2. H I K L T P t 

KLMT W P 2 

M T L K W P 3 

X H K Y Z P 4 

T W L K S P 5 

(6) A Matter of Observation and Experiment. 
On studying the problem relative to the tardiness of 
John, it appears that in obtaining the various antecedents 
the work would be largely a matter of observation. 
Carrying the father's dinner, the route through the woods, 
etc., are facts which observation would make evident. 
However, when it becomes necessary to vary these ante- 
cedents with a view to finding the invariable one, the 
procedure is experimental as well as a matter of casual 
observation. Moreover, in connection with the direct 
primary problem the question would be largely a matter 



39 2 Methods of Observation and Experiment 

of experiment; though observation would obtain as a 
subsidiary condition. We may conclude from this that 
the method of agreement involves both observation and 
experiment; and since the student will discover that the 
other methods impose similar demands, we are justified 
in designating these five special methods of induction as 
those of observation as well as of experiment. 

(7) Advantages and Disadvantages of the Method of 
Agreement. 

The concrete cases given to illustrate the method of 
agreement present a simple combination of antecedents 
and consequents. In life, however, such simplicity does 
not usually obtain and in consequence the method of 
agreement gives rise to a few serious difficulties. These 
may be summarized as (a) Plurality of causes; (b) Im- 
material antecedents ; (c) Complexity of phenomena; (d) 
Uncertainty of conclusion. 

(a) Plurality of causes is mentioned by Mill as con- 
stituting the "characteristic imperfection" of the method 
of agreement. As the term signifies, plurality of causes 
represents a condition where a given phenomenon has 
more than one cause, or where different causes produce 
the same effect. For example, "A poor crop" may be 
due to drought, neglect, pests, etc. ; heat may be caused by 
friction, electricity, combustion. Unfavorable home con- 
ditions; ill health; dislike for teacher — any one of these 
might be followed by irregular attendance. 

(b) Immaterial antecedents are those which precede 
a given phenomenon and yet, under the most favorable 
situations, have no causal connection with said phe- 



Method of Agreement 393 

nomenon. For example, the various antecedents of the 
heavy rain may have been a south wind, forgetting to 
take an umbrella, missing the car and having to walk, etc. 
Clearly these antecedents, with the exception of the first, 
are immaterial. 

(c) The law of agreement demands that all the mate- 
rial antecedents receive consideration, but often the situa- 
tion is too complex to make this possible; a fair illustra- 
tion of such would be an attempt to ascertain all of the 
antecedents of "the high cost of living." 

(d) The law of agreement never precludes the possi- 
bility of error ; as it is quite impossible to carry the analy- 
sis to the point of absolute certainty. Of all the methods, 
"agreement" is the least reliable. Despite the foregoing 
objections, however, the method is of positive value 
because of its suggestiveness ; opening the door to 
plausible hypotheses it gives the investigators a working 
basis. 

3. METHOD OF DIFFERENCE. 

(1) Principle stated. 

Says Mill, "If an instance in which the phenomenon 
under investigation occurs, and an instance in which it 
does not occur, have every circumstance in common save 
one, that one occurring only in the former; the circum- 
stance in which alone the two instances differ is the effect 
or the cause of an indispensable part of the cause, of the 
phenomenon." 

To put this in simple terms: Whatever is invariably 



394 Methods of Observation and Experiment 

present zvhcn the phenomenon occurs and invariably ab- 
sent when the phenomenon does not occur, other circum- 
stances remaining the same, is probably the cause or the 
effect of the phenomenon. 

(2) Method symbolized. 

Using the same symbols as were used in "Agreement." 
Antecedents Consequents 

A B C D P 

— BCD — 

or 

P A B C D 

_ -BCD 

In the first instance A is probably the cause of the 
phenomenon, since it is present when the phenomenon 
occurs and absent when it does not occur. For a similar 
reason, A is the effect in the second case. 

(3) Concrete illustrations. 

(A) A wise teacher in ascertaining the cause of 
John's tardiness would have suggested at once a change 
of route. Using as symbols the initial letters of the key- 
words of the antecedents in the case, the following results : 

s d h w r t 

sdh— — 

(B) First trial. 

Problem: Unprepared home work. 

Antecedents Consequents 

1. Length of lesson, ") 

2. Definiteness of lesson, | Work not properly 

3. Amount of interest shown, [ prepared. 

4. Physical condition the same. 



Method of Difference 395 



; 



Second trial. 

1. Length of lesson the same, 

2. Lesson made more definite, 
T . . V ^Work properly prepared. 

3. Interest the same, 

4. Physical condition the same. 

The foregoing symbolized: 

L D I C W 

L — I C — 

It is seen that indefiniteness of lesson assignment is the 
cause of the unprepared home work. 

(4) Advantages and disadvantages of the Method of 
Difference. 

The main difficulty attending the use of the method of 
difference is the complexity of phenomenon. The very 
nature of the method insists as an essential requirement 
that only one material antecedent shall be varied at a 
time. In life the variations are more or less confused, 
and it is often not only impossible to observe cases of a 
single variation, but frequently error comes through 
overlooking antecedents which are material to the case 
under investigation. For these reasons the Method of 
Difference is more a method of experiment than it is a 
method of observation. By controlling the circumstances 
it becomes possible to vary but one antecedent at a time, 
and also to bring into prominence all of the material 
antecedents. 

Bacon claims that all "crucial instances" are merely 
applications of the Method of Difference. By crucial in- 
stance he means any fact which will enable us to deter- 
mine at once which supposition is the correct one. For 



396 Method of Observation and Experiment 

example, the physician may not know whether it is ma- 
laria or typhoid fever till he takes a blood test ; such a test 
typifies "crucial instances." The various tests in chem- 
istry are likewise cases of crucial instances, and, in conse- 
quence, this science makes use of "Difference" more than 
any other method. 

(5) Characteristic features of Method of Difference. 

There are three distinguishing marks of the Method of 
Difference: these are, (1) The phenomenon does not 
always happen; (2) One antecedent is variable; (3) The 
other antecedents are more or less invariable. 

The following symbolizations will make these three 
characteristics evident : 

Antecedents Consequents 

(1) ABC P 

A — C — 

(2) — B C — 
X B C P 

(3) L M T K P 

L M — K — 

Agreement and Difference Compared. 

(a) The methods of Agreement and Difference are 
complementary as may be discerned by comparing their 
characteristic features: In Agreement the phenomenon 
ahvays occurs; in Difference the phenomenon does not 
always occur : In Agreement there is one invariable ante- 
cedent; whereas in Difference there is one variable ante- 
cedent : In Agreement the other antecedents are more or 
less variable; but in Difference the other antecedents are 
more or less invariable. 



Method of Difference 397 

(b) According to Mill the Method of Agreement in- 
sists that what can be eliminated is not connected; 
whereas the Method of Difference implies that what 
cannot be eliminated is connected. 

(c) The Method of Agreement is more a method of 
4 observation, since it is chiefly concerned with the dis- 
covery of causes. The Method of Difference is dis- 
tinctly a method of experiment, because its usual aim is to 
discover effects. 

(d) The Method of Agreement is so called because 
the object is to compare several instances to determine 
in what respect they agree; but in the case of Difference 
instances are compared to determine in what respects they 
differ. 

(e) The conclusions of the Method of Difference in- 
volve greater certainty than those of Agreement and, 
therefore, the former method should be adopted when 
there is a choice. 

4. THE JOINT METHOD OF AGREEMENT AND DIFFER- 
ENCE. 

(1) Principle stated. 

The uncertainty of the conclusions of Agreement 
and the impossibility at times of employing directly the 
Method of Difference, give rise to the use of the com- 
bination of Agreement and Difference known as the 
Joint Method. As stated by Mill, the principle condi- 
tioning the Joint Method is this: "If two or more in- 
stances in which the phenomenon occurs have only one 
circumstance in common, while two or more instances 



398 Methods of Observation and Experiment 

in which it does not occur have nothing in common 
save the absence of that circumstance, the circumstance 
in which alone the two sets of instances differ is the 
effect or the cause or an indispensable part of the cause, 
of the phenomenon." More briefly the notion may be 
stated in this wise: Among many instances, if one cir- 
cumstance is invariably present when the phenomenon 
occurs, and invariably absent when the phenomenon does 
not occur this circumstance is probably the cause or the 
effect of the phenomenon. 

This principle differs from the one underlying the 
Method of Difference in that the instances considered 
are more varied and more numerous. The principle of 
Difference requires but two sets of instances, while the 
Joint Method demands at least three; two when the 
phenomenon occurs and one when it does not occur. A 
study of the symbolizations and illustrations will clarify 
this distinction. 

(2) Joint Method symbolized. 

If we use circumstances and phenomenon in place of 
antecedents and consequent, then one symbolization may 
be made to stand for ascertaining either the invariable 
antecedent, or the invariable consequent. 

Circumstances Phenomenon 

1. A B C D P x 

2. A D E F ■ P 2 

3. A L M N P 3 

4. A O P Q P 4 

5- O P Q - 



The Joint Method of Agreement and Difference 399 

6. L M N — 

7. D E F — 

8. B C D — 

It is obvious that the first, second, third and fourth 
groups of instances illustrate the principle of Agreement; 
whereas the first and eighth, the second and seventh, the 
third and sixth, and the fourth and fifth illustrate in each 
case, the principle of Difference. 

(3) Concrete Examples illustrating Joint Method. 

The problem: Too much whispering. 

Antecedents Consequent 

1. Insufficient work, 

Lack of interest, iMuch whispering. 

Seated near a friend. J 

2. More work, 
Lack of interest, 
Seated near a friend. 

3. More work, 

More interest, [►Much whispering. 

Seated near a friend.) 

4. More work, 

More interest, }>Not much whispering. 

Not seated near friend. J 

5. More work, 

Lack of interest, J>Not much whispering. 

Not seated near friend. J 

6. Insufficient work, 

Lack of interest, |-Not much whispering. 

Not seated near friend.] 



Much whispering. 



400 Methods of Observation and Experiment 



►Poor recitation. 



From this it may be concluded that the undue amount 
of whispering is caused by seating particular friends near 
each other. 

The problem: Poor recitations. 

Antecedents Consequent 

i. Long lesson, 

Faulty assignment of lesson, J-Poor recitation. 
Fear of teacher. 

2. Lesson made shorter, 
Faulty assignment, 
Fear of teacher. 

3. Lesson made shorter, 

A more careful assignment, [-Poor recitation. 
Fear of teacher. 

4. Lesson made shorter, 

A more careful assignment, J-Good recitation. 
Removal of fear of teacher. J 

5. Lesson made shorter, 
Faulty assignment, 
No fear of teacher. 

6. Lesson long, 
Faulty assignment, 
No fear of teacher. 

Fear of teacher is the cause of the poor recitation. 

(4) Distinguishing features. 

Being a combination of Agreement and Difference the 
Joint Method possesses the characteristics of each, though 
more or less modified. The distinguishing marks may be 
summarized as follows : 



Good recitation. 



Good recitation. 



The Joint Method of Agreement and Difference 401 

(1) Of the first group of instances : 

(1) The phenomenon must always occur, 

(2) One antecedent must be invariable, 

(3) The other antecedents must be more or less 

variable. 

(2) Of the second group of instances : 

(1) The phenomenon must never occur, 

(2) One antecedent must be variable, 

(3) The other antecedents must be more or less 

invariable. 

Briefly, the one principle concerned is this: There 
must be an invariable conjunction between the phenome- 
non involved and the antecedent suspected of being the 
cause. 

(5) Advantages and Disadvantages of the Joint 
Method. 

Since the Joint Method permits a consideration of the 
negative aspect of the question as well as the affirmative, 
the opportunities for testing the many instances con- 
cerned are doubled. In consequence, the conclusions of 
the Joint Method are more positive than those of the 
other methods. It follows that this same opportunity to 
multiply the instances would tend to lessen the other ob- 
jections raised against the Method of Agreement; viz., 
plurality of causes, immaterial antecedents, complexity 
of phenomenon. 

The student must regard the given illustrative sym- 
bolizations and concrete examples as being of the sim- 
plest form; in life such are the exceptions rather than 
the rule. When investigating questions, like the cause of 



402 Methods of Observation and Experiment 

the high cost of living, the effect of high tariff, the reason 
for the typhoid epidemic, etc., there is often a confusion 
of circumstances which makes the Joint Method unsatis- 
factory, even though it furnishes a larger opportunity for 
the multiplication of instances. 

The strongest case which the Joint Method is able to 
present is when the negative instances repeat the positive 
in every detail, with the one exception of the variable 
antecedent. To wit: 

Strong Argument: 

Circumstances Phenomenon 

A B C P x 

ALM P 2 

— LM — 

— BC — 
Weak Argument: 

A B C F x 

ALM : P 2 

— R S — 

— TK — 
Despite the disadvantages, the conditions of the Joint 

Method are more or less ideal; since the positive branch 
of the argument suggests the hypothesis, while the nega- 
tive branch proves the accuracy or inaccuracy of such. 

5. METHOD OF CONCOMITANT VARIATIONS. 

(i) Principle stated. 

Mill's statement is this : "Whatever phenomenon varies 
in any manner whenever another phenomenon varies in a 



Method of Concomitant Variations 403 

particular manner, is either a cause or an effect of that 
phenomenon, or is connected with it through some fact of 
causation." 

To put it differently : // when one phenomenon varies 
alone, another also varies alone, the one is either the 
cause or the effect of the other. 

(2) Concomitant Variations symbolized. 
Circumstances Phenomenon 

A P 

A + a P + p 

( A+ a)-a ■ (P + p)-p 

It is evident from this that little "a" is the cause or the 
effect of little "p." To put it in concrete form : 
Let A = X number of calories of heat, 
And P = 68° F., the original temperature of room, 
" a = candle burning in room for Yi hour, 
" p = 2 F. 
Then 

Antecedents Consequent 

X no. of cal. of heat in room = 

68° F. temp, of room 
x u u « « « + burning candle _ 

68° + 2 = 70 
x (« u « « « ^.burning candle)— burning candle 

— (68°+2°)— 2°=68° 

As large "A" is increased and decreased by little "a" 

so large "P" appears to be increased and decreased by 

little "p." This strongly suggests a causal connection 

between little "a" and little "p." 

(3) Other concrete illustrations. 



404 Methods of Observation and Experiment 



Problem: To ascertain nature of sound. 

Antecedent Consequent 

Bell rung when within a glass jar 

filled with air, Loud sound. 

Some of the air pumped out of the 

jar, Sound not sg loud. 

More air pumped into jar again, Sound louder again. 
The conclusion must be that air has something to do 
with the production of sound. 

Problem: To find best feed for egg production. 

ioo lbs. beef scraps, 
ioo lbs. wheat, 
ioo lbs. oats, 
ioo lbs. corn, 

50 lbs. beef scraps, 
100 lbs. wheat, 
100 lbs. oats, 
100 lbs. corn, 

90 lbs. beef scraps, 

100 lbs. wheat, 

100 lbs. oats, 

100 lbs. corn, 

Since the variation in the amount of beef scraps is 
accompanied by a like variation in the number of eggs 
produced, it may be assumed that beef scraps are essen- 
tial to large egg production. 

(4) Distinguishing features. 

The phenomenon always occurs but in varying 
degrees ; 



30 doz. eggs. 



>2J doz. eggs. 



►28 doz. eggs. 



Method of Concomitant Variations 405 

One antecedent varies in degree ; 
The other antecedents are invariable. 

(5) Advantages and disadvantages. 

Concomitant Variations is applicable in cases when it 
is impossible to use Difference. Recourse is made to 
the latter when the phenomenon can be made to appear 
or disappear at will, but there are times when it is 
impossible to cause the phenomenon to disappear 
altogether. For example, in the case of the varying 
degrees of heat in the room it would be scientifically 
impossible to take all of the heat out of the room ; or in 
experimenting with gravitation, to do away with its in- 
fluence entirely, is beyond the power of man. It is thus 
evident that Concomitant Variations may be used in cases 
where the conditions forbid doing away entirely with 
the prenomenon. 

The special function of Concomitant Variations seems 
to be to establish the exact quantitative relation between 
the varying cause and the varying effect. To illustrate: 
As a general law it is known that bodies attract each 
other in varying degrees according to their distances 
apart and according to their relative sizes; by Concomi- 
tant Variations this law has been given definite quantita- 
tive value and reads like this : "Bodies attract each other 
directly as the product of their masses, and inversely as 
the square of the distance between them." This illus- 
tration suggests that the variation between antecedent 
and consequent may be direct or inverse. 

The error most common in this method is the assump- 
tion that the quantitative relation between two varying 



406 Methods of Observation and Experiment 

phenomena will always be according to a constant ratio. 
For example, when being reduced from a high tempera- 
ture to 39 1-5 F., water steadily contracts; but at 
39 1-5 F. it commences to expand until it becomes ice. 
Thus the ratio of contraction of water is constant only 
within certain limits. In any event the established ratio 
of variation can with absolute safety be applied only to 
the instances investigated. Another disadvantage inci- 
dent to this method, is the situation of two elements 
varying together constantly, and yet having no causal 
connection whatever. 

6. THE METHOD OF RESIDUES. 

(1) Principle stated. 

As stated by Mill the principle of residue is this: 
"Subtract from any phenomenon such part as is known 
by previous inductions to be the effect of certain ante- 
cedents, and the residue of the phenomenon is the effect 
of the remaining antecedents." 

In simpler form the notion is this: Subtract from any 
phenomenon those parts of it zvhich are known to be the 
effect of certain antecedents, and what is left of the 
phenomenon is the effect of the remaining antecedents. 

(2) Principle symbolized. 

Antecedent Consequent 

A x 

B y 

C z 

The total cause of the phenomenon xyz is ABC. 



The Method of Residues 407 

But it is known that the cause of x is the antecedent A ; 
whereas the cause of y is the antecedent B ; hence it is 
concluded that the cause of z is the antecedent C. 

(3) Concrete illustrations. 

Problem: To find the weight of coal. 

Antecedents Consequents 

Weight of driver, 
Weight of wagon, 
Weight of coal. 



= 4200 lbs. 



Weight of driver, ) __^ 200 ibs.|_ , 

Weight of wagon. \ ~^200O lbs.(" 

Hence we may conclude that the weight of coal is 
4200 lbs. — 2200 lbs., or 2000 lbs. 

Perhaps the most noted instance in history of the 
application of this method, was the one which resulted in 
the discovery of Neptune. In calculating the orbit of 
Uranus, it was found that the combined attractions of 
the sun and the known planets did not account for the 
path which Uranus took. There was some unknown 
influence at work. Assuming that this unaccountable 
attraction was due to the presence of another planet 
beyond the orbit of Uranus, an Englishman by the 
name of Adams, and later the Frenchman Leverrier, 
were able to indicate by the principle of Residues, the 
spot where this planet should be. By directing the tele- 
scope toward this point, Neptune was discovered. 

(4) Distinguishing features: 

The phenomenon always occurs, 

The antecedents are usually invariable, 



408 Methods of Observation and Experiment 

Some of the antecedents are known to be the 
cause of a part of the phenomenon. 

(5) Advantages and disadvantages. 

The Method of Residues gives three distinct results: 
First, it tells what is left over after all the other parts 
of the phenomenon have been explained. Second, it 
tells how much is left over, and third, it calls attention 
to the unexplained parts of the phenomenon. For ex- 
ample, in the first concrete illustration, by subtracting 
the known quantities from the total quantity, what is 
left over is found to be coal; not only so but we are 
able to calculate the exact amount of coal. This illus- 
trates the first and second results of the Method of 
Residues. (Like concomitant variations it is seen that 
residues is serviceable in given definite quantitative 
values.) The discovery of Neptune illustrates well the 
third result of this method; i. e., after accounting for 
every other force, it was found that there was yet a 
force at work which had never been explained. It is 
this third feature of unexplained residues which has 
placed "Science in its present advanced state." "Most 
of the phenomena which nature presents are compli- 
cated; and when the effects of all known causes are 
estimated with exactness, and subducted, the residual 
facts are constantly appearing in the form of phenome- 
na altogether new, and leading to the most important 
conclusions." So says John Herschel. Almost all of 
the discoveries in astronomy have come about in this 
way. If a heavenly body does not behave as it should 
according to the established theory, then either the 



The Method of Residues 409 

theory is wrong or there is some residual phenomenon 
which needs to be explained. Its suggestiveness is, 
therefore, the most important function of this method, 
though this very feature is the one which makes evi- 
dent its greatest disadvantage. The unexplained resid- 
ual phenomenon may be very complex and, therefore, 
a careless observer is apt to overlook a lurking element 
which in reality is the true cause. 

7. THE GENERAL PURPOSE AND UNITY OF THE FIVE 
METHODS. 

Thinking has been defined as the deliberative process 
of affirming and denying connections. It is obvious that 
these five methods are a matter of affirming and denying 
connections between antecedents and consequents. As 
soon as the looked for connections are established, the 
antecedents and consequents are known to be related to 
each other as causes and effects. In this attempt to 
find and prove connections the Method of Agreement is 
chiefly valuable in suggesting workable hypotheses, and 
the method of difference in verifying, through experi- 
ment, the correctness or incorrectness of these hypo- 
theses. 

In substance the principle conditioning both methods 
is this : "If a single antecedent is invariably present when 
the phenomenon is present and invariably absent zvhen 
the phenomenon is absent then this antecedent is the 
cause of the phenomenon." To put it still more briefly: 
Between two phenomena there is a causal connection, 
if the conjunction between the two is invariable. It is 



4io Methods of Observation and Experiment 

the business of Agreement to single out the one ante- 
cedent and of Difference to show, by presenting the nega- 
tive as well as the affirmative side of the case, that the 
conjunction of the one antecedent and the particular 
phenomenon is invariable. The Joint Method is merely 
a combination of Agreement and Difference carried into 
more varied and complex situations. The methods of 
Concomitant Variations and Residues are merely modi- 
fications of Difference; the former being used when the 
chief feature is the fluctuation of the phenomenon, and 
the latter when it is desired to find what is left over. 

Agreement suggests the hypothesis, "difference'' proves 
it; the joint method is "difference" more or less compli- 
cated, concomitant variations is "difference" applied to 
fluctuating phenomena, residues is "difference" used to 
find what and how much is left over. 

Agreement is the method of observation and belongs to 
the physician and nature student. Difference and the 
Joint Method are experimental devices which are used by 
the physicist and chemist. Concomitant Variations is the 
method of unstable phenomena and naturally attaches 
itself to the economist and statistician. Residues is the 
method of "lurking exceptions" and is favored by the 
astronomer and mathematician. Residues, being the 
method of "what is left over,'' is the most common in 
daily affairs.* 

All the five methods are forms of inductive thinking 
which lead to the establishment of causal connections by 



* All cases of finding the net proceeds are examples of the law 
of residue. 



Purpose and Unity of the Five Methods 411 

means of the principle of the invariable conjunction of 
phenomena. 

8. OUTLINE. 

The Five Special Methods of Observation and Experiment. 

(1) Aim of Five Methods. 

Fundamental fact of causation. 
Aim of analysis. 

' agreement 
difference 
Methods of \ joint 

concomitant variations 
residues 

(2) Method of Agreement. 
Principle stated 
Method symbolized 
Method illustrated 
Distinguishing features of method 
A matter of observation and experiment 
Advantages and disadvantages 

(3) Method of Difference. 
Principle stated 
Method symbolized 
Method illustrated 
Advantages and disadvantages 
Characteristic features 
Agreement and Difference compared 

(4) The Joint Method of Agreement and Difference 
Principle stated 
Method symbolized 
Concrete illustrations 
Distinguishing features 
Advantages and disadvantages 

(5) Method of Concomitant Variations 
Principle stated 
Method symbolized 
Concrete illustrations 



412 Methods of Observation and Experiment 

Distinguishing features 
Advantages and disadvantages 

(6) The Method of Residues 

Principle stated 
Method symbolized 
Concrete illustrations 
Distinguishing features 
Advantages and disadvantages 

(7) General Purpose and Unity of Five Methods 

One fundamental principle 

9. SUMMARY. 

(1) The fundamental fact of causation underlies the three 
forms of induction, but is most conspicuous in the method of 
analysis and may be ascertained by recourse to one of the 
experimental methods. 

(2) The principle of the method of agreement may be 
summed up in the two statements : The sole invariable ante- 
cedent of a phenomenon is probably its cause and the sole in- 
variable consequent of a phenomenon is probably its effect. 
These two statements may be symbolized and illustrated. 

The essential characteristics of the method of agreement are 
the phenomenon always occurs ; there is at least one invariable 
antecedent; the other antecedents vary. 

The method of agreement together with the other four methods 
may justly be termed methods of experiment as well as methods 
of observation. 

The difficulties of the method of agreement are in the main 
plurality of causes, immaterial antecedents, complexity of 
phenomenon and uncertainty of conclusion. These difficulties 
may be summarized as involving a phenomenon which may have 
several causes ; may be preceded by conditions of no causal con- 
sequence; may be so involved as to prevent exhaustive examina- 
tion; and may give unreliable conclusions. 

Agreement is valuable chiefly in furnishing to the investigator 
plausible hypotheses. 

(3) The principle of difference is this : "Whatever is in- 
variably present when the phenomenon occurs and invariably 



Summary 413 

absent when the phenomenon does not occur, other circumstances 
remaining the same, is probably the cause or the effect of the 
phenomenon." 

Like agreement, difference admits of symbolization and illus- 
tration by concrete examples. 

The chief difficulties attending difference are: in nature vary- 
ing one antecedent at a time is infrequent, and it is easy to 
overlook antecedents which are closely related to the case under 
investigation. 

Difference is the most common method of the experimental 
sciences. The characteristic features of difference are, the phe- 
nomenon does not always occur, one antecedent is variable, while 
the others are invariable. 

The methods of agreement and difference are complementary 
processes. Agreement attempts to eliminate all the antecedents 
but one, while difference aims to eliminate one only. Agreement 
is a method of observation, while difference is a method of ex- 
periment. The conclusion of the method of difference gives 
greater certainty than that of the method of agreement. 

(4) The joint method may be stated in this way: Among 
n any instances if one circumstance is invariably present when 
the phenomenon occurs and invariably absent when the phenom- 
enon does not occur, this circumstance is probably the cause or 
the effect of the phenomenon. 

The instances of the joint method are more numerous and 
more varied than those of either agreement or difference. 

The joint method has the distinguishing characteristics of both 
agreement and difference. 

Because it furnishes greater opportunities for multiplying and 
varying the instances involved, the joint method presents fewer 
objections than either of the two separate methods. 

The positive branch of the joint method suggests the hypothe- 
sis, while the negative branch proves it. This makes the method 
somewhat ideal. 

(5) The principle of concomitant variations may be stated as 
follows : If when one phenomenon varies alone, and another also 
varies alone, the one is either the cause or the effect of the 
other. This is the method of fluctuation, and is used when it is 



414 Methods of Observation and Experiment 

impossible to make the phenomenon disappear altogether, as in 
the case of difference. 

The chief function of concomitant variations is to establish 
exact quantitative relations between cause and effect. 

(6) The principle of residues is this: Subtract from any 
phenomenon those parts of it which are known to be the effect 
of certain antecedents, and what is left of the phenomenon is 
the effect of the remaining antecedent. 

The most valuable feature of residues is its suggestiveness ; an 
attempt to explain the "residual phenomenon" has led to many 
important scientific discoveries. 

(7) The five methods are concerned with the establishment 
of causal connections between phenomena. Agreement suggests 
the connection while difference proves it. The other methods 
are modified applications of difference, necessitated by some 
peculiar form which the phenomenon may take. A statement of 
the one principle involved is: "If the conjunction between two 
phenomena is invariable then there is a causal connection." 

All of the methods are forms of inductive thinking. 

10. REVIEW QUESTIONS. 

(1) Explain "the fundamental fact of causation." 

(2) Show that the fact of causation is most conspicuous in 
induction by analysis. 

(3) Name the five special inductive methods of observation 
and experiment. 

(4) State, symbolize, and illustrate the method of agreement. 

(5) Give examples of antecedents which do not function as 
causes. 

(6) Show that the "special methods" are a matter of both 
observation and experiment. 

(7) Give the distinguishing features of the method of 
agreement; illustrate by reference to the symbols. 

(8) Exemplify the plurality of causes ; immaterial antecedents ; 
complexity of phenomenon. 

(9) Show that the conclusions of agreement are largely 
hypothetical. 



Review Questions 415 

(10) State, symbolize, and illustrate the method of difference. 

(11) Show by illustration that, in the method of difference, 
only one antecedent should be varied at a time. 

(12) Show that difference is naturally a method of experi- 
ment. 

(13) Explain Bacon's use of the term "crucial instances." 

(14) Name and explain the characteristic features of the 
method of difference. 

(15) Show that agreement and difference are complementary. 

(16) Explain and illustrate the joint method. 

(17) What inference may be drawn from the following 
instances : 

Antecedents Consequents 

ALMT pqrg 

BLME zqrx 

BCME rzxy 

AM T H p q g o 

(18) "Mr. Darwin, in his experiment on cross and self fer- 
tilization in the vegetable kingdom, placed a net about one 
hundred flower heads, thus protecting them from the bees. He 
at the same time placed one hundred other flower heads of the 
same variety of plant where they would be exposed to the bees. 
He obtained the following result: The protected flowers failed 
to yield a single seed. The others yielded about 2,720 seeds. 
Thus cross-fertilization was proved." (Hibben). 

What method did Darwin employ? Symbolize the experiment. 

(19) Summarize the distinguishing marks of the joint method. 

(20) Show that the joint method is more ideal than either 
agreement or difference. 

(21) State and give concrete illustrations of the law ot con- 
comitant variations. 

(22) What is the chief function of concomitant variations? 
Illustrate. 

(23) Give instances where it would be impossible to use 
difference, but easy to use concomitant variations. 

(24) Explain this : "The quantitative variation between ante- 
cedent and consequent may be either direct or inverse." 



416 Methods of Observation and Experiment 

(25.) State and explain by illustration the method of residues. 

(26) What are the advantages and disadvantages of the 
principle of residues? 

(27) State the principle which virtually sums up the five 
methods. 

(28) Write briefly on the practical applications of the five 
methods to the ordinary walks of life. 



11. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) Trace the connection between the method of agreement 
and induction by simple enumeration. 

(2) Show that Mill's methods may properly be termed 
"Inductive Methods of Scientific Investigation." 

(3) How may it be shown by "agreement" that the high cost 
of living is due to the tendency to spend more than we earn? 

(4) Assume that you are a member of the Board of Health, 
and that you desire to ascertain the cause of the diphtheria 
epidemic by means of the principle of agreement. 

(5) What is the error involved in coming to the conclusion 
that to sit at table where there are thirteen, may mean the 
death of one of the thirteen before the end of the year. 

(O Indicate how it could be shown, by the method of 
difference, that the mosquito is responsible for the propagation 
of yellow fever. 

(7) "Another experiment similar to this was tried by Plateau, 
who put some food of which cockroaches are fond on a table 
and surrounded it with a low circular wall of cardboard. He 
then put some cockroaches on the table; they evidently scented 
the food, and made straight for it. He then removed their 
antennae." (Hibben). Complete and give with explanations the 
method used. 

(&} "In some cases it is impossible to remove an element 
which is supposed to be the cause of an effect under investigation." 
Explain and illustrate. 

(9) "Extreme care must be taken that, in the withdrawing of 



Questions for Original Thought 417 

any element, no other element is inadvertently introduced." 
Tyndale supposed he had proved spontaneous generation, when, 
after sealing in a jar of boiled water a wisp of baked hay, he 
found, after many days, indications of life within the bottle. 
In transferring the hay to the bottle, he carried the former 
across the room. What element was inadvertently introduced? 

(10) "The attempt to determine the numerical relations ac- 
cording to which two phenomena vary, requires the utmost 
caution as soon as our inference outsteps the limits of our 
observations." (Fowler). Explain this in connection with the 
law of concomitant variations. 

(11) "When the effects of all known causes are estimated with 
exactness and subducted, the residual facts are constantly ap- 
pearing in the form of phenomena altogether new, and leading 
to the most important conclusions." Make clear by illustration 
this quotation which has reference to the principle of residues. 

(12) Explain "invariable conjunction of phenomena." 

(13) Investigate by means of one of the five methods the 
following problems: 

(1) "All vegetables which grow to root should be 
planted during the last two days of the waxing 
moon." 

(2) "In this section the south wind is the storm wind." 

(3) "Mischief is the outcome of misdirected energy." 

(4) "Bad boys usually receive unjust treatment." 

(5) "An ounce of prevention is worth a pound of cure." 



CHAPTER 19. 

THE AUXILIARY ELEMENTS OF INDUCTION. 
OBSERVATION EXPERIMENT HYPOTHESIS. 

1. THE FOUNDATION OF INDUCTIVE GENERALIZA- 
TIONS. 

Induction is the process of universalizing particular 
facts. The starting point is the fact. Through observa- 
tion the investigator gathers facts, and then works them 
over with a view of finding uniformities. The mind 
cannot build inductive generalizations without facts any- 
more than a mason can build a brick wall without the 
bricks. 

A fact is any particular thing made or done or is that 
which may be acquired by means of the presentative 
(perception and imagination) powers of the mind. The 
state of awareness which results from the observation of 
facts is an individual notion. This presents another 
aspect of the inductive process ; namely, "It is a matter of 
building general notions from individual notions, acquired 
by the observation of facts." To illustrate: I note that 
A, B, C and D are honest in their dealings with me, hence 
I come to the conclusion that some men are honest. A 
fact is something done, consequently the actual doing of 
the honest things by A, B, C and D are facts. Each state 
of awareness of each fact is an individual notion. The 
mind now discerns a uniformity in these facts and de- 
rives the general notion that "some men are honest." 

418 



Observation 



419 



2. OBSERVATION. 



Facts are acquired by means of observation. When 
the mind fixes the attention upon any phenomenon it 
observes it. The term observation means "to watch for" 
and may be defined as the act of watching for phenomena 
as they may occur. The observation may be only casual, 
or it may be willed or rational. It is the latter aspect 
which most concerns the logician. In this sense observa- 
tion means careful, painstaking, systematic perception. 
It involves the concentration of consciousness upon the 
case in hand, or the actual giving of attention. The 
thing observed may be external, when the observation 
takes the form of sense-perception; or it may be internal, 
when the observation becomes a matter of introspection. 

3. EXPERIMENT. 

In observation we simply watch the phenomenon; in 
experiment we make it. In experiment we not only ob- 
serve, but we manipulate the circumstances so as to pre- 
sent the phenomenon under the most favorable condi- 
tions for observation. "In observation," says Mill, "we 
find an instance in nature suited to our purposes" ; whilst 
in experiment, by an artificial arrangement of circum- 
stances, we make an instance suited to our purpose. In 
observation we watch for causes ; in experiment we work 
for effects. We may thus define experiment as the act 
of making phenomena occur for the purpose of watching 
for effects. In experiment there is much which is merely 
observation. In fact experiment is observation in which 
the phenomenon is artificially produced. For the sake 



420 The Auxiliary Elements of Induction 

of definiteness, however, any observation which involves 
a manipulation of circumstances, may be designated as 
experimental. 

4. RULES FOR LOGICAL OBSERVATION AND EXPERI- 
MENT. 

To the uninitiated, the matter of observation seems an 
easy task, and yet when one hears two honest men swear 
to diametrically opposite facts which have come to them 
from observing the same phenomenon, his faith is 
shaken. "Eyes have they but see not" is a logical truth 
as well as a moral one. Only the observation of the 
trained can be depended upon; and yet this should not 
discourage the layman, for even he, by a little conscien- 
tious effort towards careful observation, may greatly 
increase his store of accurate knowledge and add to the 
joy of living. 

The attending rules are usually heeded by the trained 
scientist in matters of observation and experiment: 

First Rule. The observations should be precise. The 
time, the place, the surrounding conditions must be ac- 
curately noted. Many artificial contrivances have been 
devised because of the desire of the scientist to be pre- 
cise. Instruments like the balance, the thermometer, the 
microscope, etc., has he invented, and various devices 
and methods has he adopted for the sake of precision. 
A common method is to take an average of observations. 
For example, to estimate justly the class work of a 
student, the teacher should not be content with the ratings 
of one or two recitations, but must average the ratings of 



Rules for Logical Observation and Experiment 421 

many recitations. Again, a child may be led to discover 
approximately the value of the sum of the interior angles 
of a triangle by measuring the angles of many triangles 
and then striking an average; assume that the following 
results are obtained by such a procedure: (1) 178, (2) 
181, (3) 179, (4) 180, (5) 182; adding these and divid- 
ing by 5 gives 180. 

Second Rule. The observations should concern only 
the material circumstances of the case in hand. All the 
non essentials may be ignored, as they serve only to dis- 
tract attention. For example, (1) in order to get the 
"right count" all other sounds must be ignored save that 
of the fire gong; (2) in finding the depth of the water 
for the building of a dam, soundings ten miles away from 
the objective point could be of little value. On the other 
hand, it is easy to overlook certain lurking essentials. To 
observe such, it is necessary to resort to what the psy- 
chologist terms a "preadjustment of attention." We 
must know with exactness what we are looking for. We 
must have a mental image of what we wish to see. The 
astronomer in the discovery of a new planet must know 
the exact spot where it ought to be, and have a clear 
mental image of its appearance. This expectant attention 
is a necessity in the case of the physician who is anxious 
to make no mistakes in his diagnosis. If he is looking 
for pneumonia, he must have a very distinct auditory 
image of the sound of an affected lung. It should be re- 
marked, however, that this very preadjustment of atten- 
tion, with the untrained, frequently leads to illusion. We 
are so anxious to see what we are looking for that nine- 



422 The Auxiliary Elements of Induction 

tenths of what we believe we see is only inference. How 
easy it is to read into a phenomenon something that is 
entirely foreign to it; to read between the lines; to see 
only the reflection of our own ideas. "Verily the mental 
picture of what we wish to see becomes so vivid that we 
are positive of the thing being external." Thus the 
drunkard sees snakes and the superstitious see ghosts. 
Reading into the external what is only vivdly internal is 
probably the most common error with the untrained 
observer. 

Third Rule. The observed circumstances should be 
varied as much as possible. To observe a fact from a dif- 
ferent viewpoint may not only broaden the original no- 
tion, but it may change it entirely. In order to gain a 
true notion of the effect of a particular nostrum on the 
human organism, it becomes necessary to experiment 
with persons of different ages, living under different 
environments, and inheriting different constitutions. 
Those who are noted for pronouncing broad, safe and 
sane judgments upon momentous questions are those who 
are "all-angled observers." 

Fourth Ride. The observed phenomenon should, if 
possible, be isolated from all interfering phenomena. 

In studying the action of a drug or a food, all other 
drugs or foods must be eliminated. The effect of gravita- 
tion on a body cannot be recorded accurately unless the 
experiments are made in a vacuum. When studying the 
deflections of the compass, all magnetic substances must 
be removed from the field. 



Common Errors of Observation and Experiment 423 

5. COMMON ERRORS OF OBSERVATION AND EXPERI- 
MENT. 

The rules for scientific observation have suggested cer- 
tain common errors which may now be considered. 

(1) Preconceived ideas. 

There is not an unholy belief nor an unwholesome 
theory which cannot be bolstered up by means of ap- 
parent facts. For example, that monstrosity of Puritan 
thought known as "Salem Witchcraft" was substantiated 
by facts honestly observed. Again, having made up his 
mind that it is going to be "so and so," the statistician 
goes out into the highways and byways and gathers the 
facts which vindicate his judgment. Further, the demo- 
crat finds that the majority of the voters are democrats; 
while the republican is confident that two-thirds of the 
voters are for republicanism. Here again is the fallacy 
springing from a preadjustment of attention. We see 
what we want to see. Only the highly trained observer 
is able, with impunity, to make use of preadjusted atten- 
tion, and even with him, it is not easy to remove from 
the situation belief and prejudice. 

The true observer undertakes his work with his mind 
open to anything which the eye may bring him, though it 
may topple into the dust his dearest theory and most 
cherished belief; he proceeds — the mind a "clean white 
page. }} 

(2) The "observed" and the "inferred" confused. 
This error has already received some attention. It may 

be remarked further, however, that, psychologically con- 
sidered, observation is a matter of interpreting the new 



424 The Auxiliary Elements of Induction 

by means of the old. Of necessity the interpretation, 
whatever it may be, will assume the complexion of the 
particular "old knowledge" which the mind is able to 
use. In short, a man will see what his previous environ- 
ment has trained him to see; the conscientious gardener 
sees the weeds, whilst the artist may see nothing but the 
flowers. It follows, therefore, that all observation must 
be largely a matter of inference based on experience. 
In looking at the moon, for example, all I actually see is 
a patch of color; the form and distant location of the 
moon being a matter of experience. 

The inference referred to in this heading is not that 
which is necessary for perception, but that which is sug- 
gested by perception. To illustrate : It is icy ; three men 
are running for a car; Smith raises his arm; Jones slips 
to the ground; and Brown testifies, that "Smith knocked 
Jones down." Brown observed, that Smith assumed the 
proper attitude and that Jones conveniently went down at 
the right time ; and then inferred the rest. 

(3) Ignoring the exceptions. 

This comes through an over anxiety to prove our 
theory. With this mental attitude, the observations which 
are corroborative will so completely fill the mental field, 
that the exceptions are made to seem of no consequence. 
This accounts for the superstition attached to thirteen: 
As a coincidence some one at some time died who had 
previously eaten at a table where there were thirteen. 
Perhaps during the life of the superstitious one this hap- 
pened on two or three occasions, but the fact so im- 
presses the subject that he ignores the dozen times when 



Common Errors of Observation and Experiment 425 

death did not follow. Other generalizations belonging to 
this class are (1) people never die at flood tide; (2) 
there must be three accidents in succession; (3) the first 
sight of the new moon over the right shoulder is a good 
omen ; (4) seeds which grow to root do best when planted 
during the last days of the waxing moon; (5) horse 
chestnut in pocket guards against sore throat, etc. 

(4) Sympathy and undue interest. 

The influence of the heart over the brain is well known. 
A physician is liable to this error when he attempts to 
prescribe for one of his own family. Sympathy not only 
warps the judgment but it may actually interfere with the 
accuracy of an honest observer's perceptive powers. 

(5) Inattention and a fallible memory. 

These short comings are too apparent to demand dis- 
cussion. 

6. THE HYPOTHESIS. 

Having observed the facts, the mind naturally seeks 
for explanation of the same. Hence taking the facts as 
a cue and bringing into play a constructive imagination, 
a plausible supposition is advanced, which is then proved 
or disproved. Such a supposition is known as an 
hypothesis. 

Definition. An hypothesis is a supposition advanced 
for purposes of explanation and proof. 

First illustration. The facts are known that light 
travels from the sun to the earth, and at the rate of 186 
thousand miles per second. These facts suggest the prob- 



426 The Auxiliary Elements of Induction 

lems: (1) How does the light reach the earth? (2) 
Why this rate of speed ; why so much faster than the rate 
at which sound travels? To solve these problems, or to 
explain the facts, the "ether" hypothesis is advanced: 
viz., "A rare medium called ether pervades space and 
transmits the light and heat of the sun." This hypothesis 
has never been conclusively proved. 

Second illustration. Fact : The child leans forward and 
squints his eyes, when attempting to read work which has 
been placed on the black board ; hypothesis : The child is 
near sighted. 

7. INDUCTION AND HYPOTHESIS DISTINGUISHED. 

Induction is a matter of realizing generalizations from 
the observation of facts. The product of such is an in- 
duction, but we know that an hypothesis is likewise a 
generalization based upon facts. What is the difference ? 
An induction, as such, is a broader term than hypothesis. 
As soon as the hypothesis is proved or disproved, it 
ceases to be an hypothesis, but still remains an induction. 
An hypothesis, being advanced for purposes of explana- 
tion ceases to be an hypothesis when, in the last analysis, 
it fails to explain. Moreover, as soon as the hypothesis 
is shown to be an undoubted truth, it also loses its dis- 
tinctive hypothetic marks. An hypothesis is merely a 
tentative induction. 
Illustrations : 

(1) The hypothesis is advanced that the fire started 
from the coal range in the kitchen. After the incendiary 
is caught, this supposition ceases to be an hypothesis. 



Induction and Hypothesis Distinguished 427 

(2) It is suspected, that my insomnia is due to the 
three cups of strong coffee indulged in at the evening 
meal. As soon as this supposition is proved by experi- 
mental means (law of difference), it ceases to be an 
hypothesis and becomes an unpopular inductive truth. 

8. HYPOTHESIS AND THEORY. 

In common parlance hypothesis and theory are used 
interchangeably. We refer to the "nebular hypothesis" 
or the "nebular theory" ; to the "hypothesis of the sun's 
heat" or "the theory of the sun's heat." On the other 
hand, we say "the theory of gravitation," "the theory of 
evolution," etc., with certain uniformity. From these 
observations we may infer that hypothesis and theory 
may be used interchangeably when the facts are of a 
low probability; but when the facts have undergone 
cogent verification, it is more correct to use theory in 
their designation rather than hypothesis. "A theory is a 
partially verified hypothesis." It has been remarked that 
theory has a second signification of being a term which 
stands for "any body of acquired truth." It is unfor- 
tunate that its use could not be confined to this latter 
conception. 

9. THE REQUIREMENTS OF A PERMISSIBLE HYPOTHE- 

SIS. 

Any hypothesis should be made to conform to the fol- 
lowing requisites: (1) The hypothesis must be con- 
ceivable. The hypothetic generalizations of primeval days 
were mere fancy. For example, the loud noise from the 



428 The Auxiliary Elements of Induction 

clouds on dark days was the angry voice of the God of 
the skies. Even in this day when a complex situation 
cannot be explained there comes the temptation to draw 
entirely upon the imagination, and advance an hypothesis 
which is absurd in every sense of the word. The per- 
missible hypothesis demands that there be some ground 
for the conjecture. A fact or two at least must be used 
as the foundation for whatever the constructive imagina- 
tion may build. On the other hand the past has taught 
us that we cannot afford to be too exacting in the enforce- 
ment of this rule. The ideas of Copernicus, Newton, 
Harvey, Darwin, and many another of the world's best 
thinkers, were looked upon at first as being ridiculous. 
There is always a bare possibility of a "lurking truth" 
in the conjecture, and no broad minded and sanely edu- 
cated man can afford to scoff blindly at something which 
may seem to him mere fancy. Prejudice and a willful 
blindness to truth, have ever been imminent stumbling 
blocks in the path of progress. 

(2) The hypothesis must be capable of proof or dis- 
proof. This means, that where it is possible the hypoth- 
esis should touch, in one form or another, our experi- 
ence. If the hypothesis is wholly unlike any experience 
we may have had, it becomes impossible to ascertain, 
whether it agrees or disagrees with the facts, which it is 
supposed to explain. A legitimate hypothesis must 
furnish some opportunity for securing facts to prove or 
disprove it. For example, to advance an hypothesis rela- 
tive to the conditions of the next world is hardly per- 
missible, as "spirit-facts" are entirely without our field 



The Requirements of a Permissible Hypothesis 429 

of experience. Surely, one returning from Heaven could 
give us no conception of it; because there is nothing in 
the carnal mind that may be used to interpret the experi- 
ences that must function in the Celestial City. 

(3) The hypothesis must be adequate. It should 
take into consideration all the known facts. It stands to 
reason that, if one known fact is ignored, the entire pro- 
cedure is thus vitiated. It would be absurd to suppose the 
moon to be inhabited without giving heed to the fact of 
its having no atmosphere. 

(4) The hypothesis must be as simple as possible. 
We must, of course, recognize situations which in them- 
selves are too complex to admit of simple conjectures. 
The purport of the fourth rule is, that the hypothesis 
should not be made unnecessarily complex. 

(5) The hypothesis should not contradict any verified 
truth. Any conjecture which opposed the law of gravita- 
tion would be out of place. Of course it is possible to 
have only apparent conflicts between the new hypothesis 
and the old law. Further observation should show that 
no such clash exists. 

10. THE USES OF HYPOTHESES. 

The hypothesis is serviceable mainly in these par- 
ticulars : 

(1) As a working basis. 

When one is confronted with a huge mass of facts it 
becomes necessary to start somewhere, and with as little 
waste of time and energy as possible. Almost anything 
is better than a haphazard floundering which reaches 



430 The Auxiliary Elements of Induction 

"nowhere." So the investigator hazards a tentative theory, 
which he at once proceeds to verify. If verification fails, 
then he may discard this first hypothesis for a better one. 

(2) As a guide to ultimate truth. 

Much might be said relative to the use of rejected 
hypotheses. By means of these, science has advanced 
step by step towards the full light of perfect knowledge. 
As has been remarked, no true scientist cares to overlook 
the opportunity for suggestive inspiration which some 
forsaken hypothesis may afford him. Just as the indi- 
vidual attains the best success by using his failures as 
stepping stones, so the true scientific discoverer climbs up 
to the light on the stairway of discarded hypotheses. By 
testing and rejecting the false hypotheses, the situation 
becomes more definite and the problem more accurately 
defined. "Kepler himself tried no less than nineteen 
different hypotheses before he hit upon the right one, 
and his ultimate success was doubtless in no slight degree 
due to his unsuccessful efforts." 

(3) As a discoverer of immediate truth. 

Often, moreover, the hypothesis leads directly to posi- 
tive verification. The supposition advanced may hit the 
truth squarely ; and may be of such peculiar nature as to 
lead easily to clear and conclusive proof. 

(4) As affording a probable explanation of a problem 
which will not lend itself to an entirely satisfactory 
solution. 

The theory of evolution may illustrate this fourth use ; 
while the history of the discovery of Neptune illustrates 
the third. 



Characteristics Needed by Investigators 431 

11. CHARACTERISTICS NEEDED BY SCIENTIFIC INVES- 
TIGATORS. 

The hypothesis is referred to "as the great instrument 
of science." The greatest thinkers of time have possessed 
the courage and the conscience to step from the known 
to the unknown; to hazard a guess as to the meaning 
of what they saw, and then subject their guess to a rigor- 
ous test. This procedure involves three elements on the 
part of the investigator : ( 1 ) Power of accurate observa- 
tion. (2) Constructive imagination. (3) A passion for 
truth. 

( 1 ) An hypothesis formed without an accurate knowl- 
edge of facts is not only useless, but often it may 
work positive harm. To advance serviceable suppositions 
which are not grounded on fact, is as impossible, as it is 
to build a house without a foundation. The hypothesis 
is an image of the constructive imagination, but the 
pedestal of this image must rest on the ground of fact. 
The investigator who would be scientific must exercise 
scrupulous care in securing his facts through observation 
and experiment. The rules and errors involved in such 
a procedure have received sufficient attention. 

(2) After the investigator has his facts to build 
upon ; and these may be few or many — sometimes even a 
single fact is sufficient — then may he theorize as to a 
possible explanation of them. Here is where the real 
work of the born genius tells. To some the facts are 
nothing but words, to others they mean universal laws 
and great inventions. Who but a Newton could have 
seen the law of gravitation in the falling apple? Who 



432 The Auxiliary Elements of Induction 

but an Edison could have seen the phonograph in the 
sound wave and wax? It must be recognized that this 
remarkable imaginative insight is inborn in some cases ; 
and yet this does not preclude the necessity for cultivating 
this power, though it may be only in a rudimentary state. 
Here is another opportunity for the school teacher; 
namely, to train in every legitimate way the constructive 
imagination. 

(3) Having once constructed the hypothesis, the hon- 
est scientific investigator at once proceeds to subject it 
to a series of most rigorous tests. It is well to see big 
things in a little fact; to have a mind as fertile in new 
ideas as a watered garden — this is genius! But is it not 
more incumbent to have a conscience so keen, that nothing 
will be allowed to pass for truth which has not received 
ample verification? Intellectual dishonesty is quite as 
common as moral dishonesty. Moreover, one must main- 
tain an open mind, absolute candor, and a willingness to 
abandon the most cherished theory. Often it is much 
easier to explain away contradictory facts than it is to 
forsake a pet theory. 

12. OUTLINE. 

The Auxiliary Elements in Induction — Observation — 
Experiment — Hypothesis. 

(1) The Foundation of Inductive Generalizations. 

(2) Observation. Defined. 

(3) Experiment. Defined. 

Compared with Observation. 

(4) Rules for Logical Observation and Experiment. 

Their need. 



Outline 



433 



First Rule. 
Second Rule. 
Third Rule. 
Fourth Rule. 

(5) Common Errors of Observation and Experiment. 

(1) Preconceived Ideas. 

(2) Confusing the Observed with the Inferred. 

(3) Ignoring the Exceptions. 

(4) Sympathy and Undue Interest. 

(5) Inattention and a Fallible Memory. 

(6) The Hypothesis. 

Denned and Illustrated. 

(7) Induction and Hypothesis Distinguished. 

(8) Hypothesis and Theory Distinguished. 

(9) The Requirements of a Permissible Hypothesis. 

(1) Conceivable, (2) Capable of proof or disproof, 
(3) Adequate, (4) Simple, (5) Not contra- 
dictory. 

(10) Uses of Hypothesis. 

(1) A working basis, (2) Guide to ultimate truth, (3) 
Discoverer of immediate truth, (4) Probable 
explanation. 

(11) Characteristics Required by Scientific Investigators. 

(1) Accurate observer, (2) Constructive imagination, 
(3) Passion for truth. 

13. SUMMARY. 

(1) Facts are the foundation of all inductive generalizations. 
Induction is largely a matter of building general notions from 
individual notions derived from the observa ion of facts. 

(2) Observation is the act of watching the phenomena as they 
may occur. It involves the voluntary concentration of c mscious- 
ness on the case in hand. 

(3) Experiment is the act of making phenomena occur for 
the purpose of watching for effects. It is in reality a form of 
observation which necessitates a manipulation of circumstances. 



434 The Auxiliary Elements of Induction 

(4) The average man is not given to careful observation. 
The rules adopted by scientific observers are: (1) The observa- 
tion should be precise; (2) should concern only the material 
circumstances; (3) should be varied; (4) should be isolated. 

For the sake of precision many instruments have been invented 
and methods devised; notably instruments for accurate measure- 
ments, such as the balance and thermometer, and methods like 
the method of averages. 

Frequently a situation may be so complicated as to demand a 
"preadjustment of attention." With the untrained this very pre- 
adjustment may lead to serious error. 

An "all-angled observer" is the most trustworthy. 

(5) Errors in observation come from preconceived ideas; 
confusing perception with inference; ignoring the exceptions; 
sympathy; inattention; and a fallible memory. 

(6) An hypothesis is a supposition advanced for purposes of 
explanation and proof. 

(7) An hypothesis is a tentative induction. As soon as it is 
deprived of its tentative nature it ceases to be an hypothesis. 

(8) Hypothesis and theory are often used interchangeably 
when reference is made to phenomena of low probability. Theory 
should be used only in instances of high probability. 

(9) A permissible hypothesis must be (1) conceivable; (2) 
capable of proof or disproof; (3) adequate; (4) simple; (5) 
must not contradict any verified truth. 

(10) The hypothesis is especially serviceable in these ioui 
particulars: (1) as a working basis; (2) as a guide to ultimate 
truth; (3) as a discoverer of immediate truth; (4) as affording 
probable explanations. 

(11) There are certain characteristics which an honest and 
courageous investigator needs to possess. These are: (1) un- 
doubted ability as an accurate observer of facts, (2) a con- 
structive imagination, (3) a passion for truth. 

To build an acceptable hypothesis without fact is as impossible 
as it is to build a house without a foundation. 

The genius, because of his imaginative insight, transforms the 
simple fact into a complex invention or law. 

A prevailing "intellectual dishonesty" suggests the need of 
"a greater passion for truth." 



Review Questions 435 

14. REVIEW QUESTIONS. 

(1) Show that facts are the raw material of induction. 

(2) Define and illustrate a fact. 

(3) Define induction in terms of the notion. 

(4) Define and illustrate observation. 

(5) Define and illustrate experiment. 

(6) Show the difference between observation and experiment. 

(7) State and exemplify the rules for logical observation and 
experiment. 

(8) Illustrate the method of averaging observations. 

(9) Explain "preadjustment of attention." 

(10) What is the most common error with the untrained 
observer? Explain and illustrate. 

(11) Explain the expression "all-angled observer." 

(12) State and exemplify the errors of observation and ex- 
periment. 

(13) To what error in observation are superstitions generally 
due? 

. (14) Define and illustrate hypothesis. 

(15) Indicate the difference between an hypothesis and an 
ordinary induction. 

(16) When may theory and hypothesis be used interchangeably? 
Illustrate. 

(17) Show by illustration that the term theory is ambiguous. 

(18) Summarize the requirements of a permissible hypothesis. 
Illustrate. 

(19) Select some school room experience with a view of mak- 
ing it conform to the requirements of a permissible hypothesis. 

(20) Explain and illustrate the uses of hypothesis. 

(21) "The scientific discoverer climbs up to the light on the 
stairway of discarded hypotheses." Explain. 

(22) Write a short theme on "Characteristics Required by 
Scientific Investigators." 

15. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 

TIGATION. 

(1) "Land and sea breezes are due to a difference in tem- 
perature." Is this a fact or a law? Explain your position. 



436 The Auxiliary Elements of Induction 

(2) Give three different definitions of induction. Which one 
have you adopted? Defend your position. 

(3) Define and illustrate observation. 

(4) Distinguish between observation and attention. 

(5) "In observation we find, in experiment we make" What 
is meant by this? 

(6) Give illustrations of falsehood due to careless observa- 
tion. 

(7) Argue for and against the use of "expectant attention" 
in observation. 

(8) "Nine-tenths of what we see comes from within." Do 
you believe this? Labor the question. 

(9) Offer suggestions which, if followed, should lead to 
scientific observation. 

(10) "One must be just before he is sympathetic." Relate this 
to the fine art of accurate observation. 

(11) Is an hypothesis a generalization? Explain. 

(12) Give school room examples of hypotheses which lead to 
injustice. 

(13) "An hypothesis is merely a tentative induction." Make 
clear this assertion. 

(14) Illustrate inconceivable hypotheses by drawing on your 
knowledge of ancient history. 

(15) "Prejudice and willful blindness to truth have ever been 
imminent stumbling blocks in the path of progress." Expatiate 
upon this. 

(16) Are the hypotheses advanced concerning communications 
from the spiritual world capable of proof or disproof? Give 
reasons. 

(17) Show by historical examples the use of discarded 
hypotheses. 

(18) "Genius is another name for hard work." Do you 
agree? Defend your position. 

(19) "The man to whom nothing ever occurs is unlikely to 
make any important discoveries." Discuss this. 



CHAPTER 20. 



LOGIC IN THE CLASS ROOM. 



1. THOUGHT IS KING. 

"Our habits make or unmake us." "In a thoughtless 
hour a groove is imbedded in the nerve substance, and 
thereafter, nine-tenths of the life flows through that 
groove." Habit is, indeed, a most powerful and a most 
tyrannical master; and yet it has come within the ob- 
servation and even the experience of many, that thought 
is even more masterful than habit. Appearing at the psy- 
chological moment and in a pedagogical way, a thought 
may be made to possess the mind with force sufficient to 
break almost any habit. From an ethical point of view, 
the exceptions to this are due to an inability to arouse 
thought of sufficient strength. Moreover, mental re- 
actions which result in habit are originally brought about 
through some thought process. Speaking in general 
terms, it may be affirmed that thought makes habit and 
if sufficiently strong breaks habit. That our habits make 
or unmake us may be true, but is it not likewise true that 
our thoughts make or unmake our habits? 

Thought is king; thought has made man king of the 
animal kingdom, and if thought has figured so largely in 
the evolution of the human animal in past ages, may we 
not assume that it will sway the future ages in like 
manner? Thought is a product of the class room. Here 
thoughts which make habits, and thoughts which break 

437 



438 Logic in the Class Room 

habits have full sway. As the children of the American 
schools think to-day, so will the men of American life 
think on the morrow; and as America thinks so will she 
ultimately do. This lends vital import to any object 
which may either inspire or regulate thought. 

2. SPECIAL FUNCTION OF INDUCTION AND DEDUCTION. 

As commonly treated logic is a regulative subject. 
This implies the two aspects of direction and correction. 
Logic directs by means of the laws and forms of thought, 
and corrects by means of the rules of right thinking. To 
a certain degree both departments of logic are directive 
as well as corrective ; but it is worthy of remark that in- 
ductive logic emphasizes the former, while deductive logic 
lays stress upon the latter. It is inductive logic which 
shows how man has acquired new knowledge; inductive 
logic explains the mode of procedure adopted by the dis- 
coverer and the inventor. On the other hand, deductive 
logic is distinctly a science of criticism. Induction directs 
to new truth; deduction aims to modify and correct new 
truth. 

3. TWO TYPES OF MIND. 

Though there are many special forms of thought, yet 
there are but two general forms; namely, induction and 
deduction. Inductive thought seeks the new; deductive 
thought corrects the old. Similarly, there are two types 
of mind : the inductive type and the deductive type. The 
former reaches out for new things, the latter is satisfied 
with ordering the old. In politics the man with the in- 
ductive type of mind becomes a "Liberal" or a "Progress- 



Two Types of Mind 439 

ive"; while the man with the deductive type of mind 
becomes a "Conservative" or a "Standpatter." It must be 
conceded that both are needed in the development of the 
best form of Democracy. We need an unfettered free- 
dom as advocated by Jefferson; but we also need an 
ordered freedom as taught by Hamilton. 

4. TOO MUCH CONSERVATISM IN SCHOOL ROOM. 

Since the beginning these two mental types have been 
in evidence — the liberal who wants to do things, and the 
conservative who wants to weigh things. With the liberal, 
it is fight whether or no ; with the conservative, it is fight 
provided the enemy is not too formidable. The one 
dares; the other cautions: both are needed to balance the 
world. 

Liberalism and conservatism may be fostered in the 
school room, and to maintain a true balance each must 
receive its share of attention. Is such the case? The 
passing of "district-school-individualism and the coming 
of "graded-school-collectism" has transferred the em- 
phasis from liberalism to conservatism — from the in- 
ductive type to the deductive type. In this day it seems 
to be more important to have the child's work orderly. 
than to have it original. In the main, examination 
papers call for correct knowledge and not for thought; 
in the main, promotions are based on accuracy, not on 
initiative. The conservative type being in control, the 
schools are sending out too many "Decluctives," not 
enough "Inductives." The world needs more Columbuses 
and Edisons. 



440 Logic in the Class Room 

5. THE METHOD OF THE DISCOVERER. 

A change must come. The methods of instruction are 
too didactic and not sufficiently inspirational. Greater 
attention must be given to the spirit of discovery and less 
to the spirit of correction. The teacher must lead less 
and follow more; must correct less and suggest more; 
must tell less and direct more. If we are to give greater 
attention to the training of discoverers, logic may aid in 
this crusade by calling attention to the common mode of 
procedure which the discoverers of the past have adopted. 
This is a legitimate topic for the logician, since induction, 
deduction, hypothesis, and proof have ever been common 
tools in the discoverer's workshop. With a view to 
becoming better acquainted with the common mode of 
procedure of the man who seeks for new truth, let us 
study two typical instances : 

(1) The Discovery of Neptune. 

The discovery of Neptune was a double one. Early in the 
present century it was found that Uranus was straying widely 
from his theoretic positions, and the cause of this deviation was 
for a long time unsuspected. Two astronomers, Adams in Eng- 
land and Leverrier in France, the former in 1843 and the latter 
in 1845, undertook to find out the cause of this perturbation, on 
the supposition of an undiscovered planet beyond Uranus. 
Adams reached his result first, and the English astronomers 
began to search for the suspected planet with their telescopes, by 
first making a careful map of all the stars in that part of the 
sky. But Leverrier, on reaching the conclusion of his search, 
sent his result to the Berlin observatory, where it chanced that 
an accurate map had just been formed of all the stars in the 
suspected region. On comparing this with the sky, the new 
planet, afterward called Neptune, was at once discovered, 23d 
September, 1846. 



Too Much Conservatism in School Room 441 

(2) Bees are guided in their flight by a knowledge of their 
surroundings, not by a general sense of direction. 

"M. Romanes took a score of bees in a box out to sea, where 
there could be no landmarks to guide the insects home. None of 
them returned home. Then he liberated a second lot of bees on 
the seashore and none of these returning, he liberated another 
lot on the lawn between the shore and the house. None of these 
returned, although the distance from the lawn to the hive was 
not more than two hundred yards. Lastly he liberated bees in 
different parts of the flower garden on either side of the house, 
and these at once returned to the hive." (Hibben.) 

A multiplication of instances would only give stronger 

evidence to the fact that the mode of procedure adopted 

by the discoverer and inventor conforms to these three 

general steps: (1) antecedent facts, (2) forming an 

hypothesis, (3) verification. It will be to our advantage 

to study somewhat in detail these three steps. 

(1) Antecedent facts. 

In the discovery, of Neptune the decisive or crucial fact 
was the knowledge that Uranus deviated from his true 
path about the sun. This knowledge was obtained 
through observation and mathematical calculation. But 
the hypothesis of the existence of another planet could 
not have been formed had it not been for the more funda- 
mental facts of inertia, gravitation, falling bodies, etc. 
For the sake of definiteness antecedent facts may thus 
be divided into foundation facts and crucial or decisive 
facts. The latter are an outgrowth of the former. The 
foundation fact of the second illustration is Romanes' 
knowledge of animal instinct; while the crucial fact is, no 
doubt, the observation that bees fly in a circle before 
starting for home. In the case of Newton's discovery of 



442 Logic in the Class Room 

the law of gravitation, the falling of the apple was the 
crucial fact; while his knowledge of terrestrial gravity 
proved to be the vital foundation fact. 

A crucial fact is one which leads immediately to the 
formation of a reasonable hypothesis. It is not to be 
inferred from this that the same fact becomes a crucial 
one to all alike. The falling of the apple was only crucial 
to a genius like Newton. With the average only extraor- 
dinary facts become crucial; but with the genius any 
ordinary fact may become crucial. Both the scholar and 
the genius may have the foundation facts, but only the 
latter may be able to read into a dry fact or event, a new 
world of truth. 

(2) Forming an Hypothesis. 

From the viewpoint of logical correctness, the matter 
of hypothesis has received due attention in an antecedent 
chapter; we need now to look at the subject through the 
eyes of the discoverer, not the logician. The crucial fact 
at first creates an intellectual perplexity which is accom- 
panied with an uneasy, dissatisfied state of mind. This 
unsatisfied feeling drives the intellect to protracted 
thought. As a final result some hypothesis is constructed 
which seems to explain the crucial fact. Here is where 
analogy functions in a most vital manner. No hypothesis 
is forthcoming unless it resembles the crucial fact. It has 
been remarked elsewhere that analogy is the basic element 
in the forming of hypotheses. So it transpires, that the 
protracted thought referred to, is virtually a mental ef- 
fort to detect significant resemblances between the well 
known crucial fact, and some hypothetical fact which the 



Too Much Conservatism in School Room 443 

imagination may picture. To put it differently: The 
crucial fact arouses a mental state of unrest which in 
turn drives the mind to a "still hunt" for relations. The 
establishment of the hypothesis is simply a makeshift, 
designed to satisfy this "mental urge." In the discovery 
of Neptune the crucial fact, the deviation of Uranus, 
produced a state of uneasiness in the minds of the as- 
tronomers. Surely something was wrong. This urged 
them to further meditation, which finally resulted in the 
hypothesis that there must be an unknown planet beyond 
the orbit of Uranus. They assumed, of course, that the 
relation between this supposed planet and Uranus was 
analogous to the relation between any two of the known 
planets. In the case of Newton the falling apple stirred 
his astute mind to the assumption that the same force 
which pulled the apple, likewise pulled the moon towards 
the earth. Here we have again (1) the crucial fact, (2) 
the mental urge, (3) the analogous hypothesis. 

(3) Verification. 

Forming an hypothesis only partly fulfills the demands 
of an unsatisfied intellect. The true discoverer, being 
possessed with a passion for truth, seeks for "the truth, 
the whole truth, and nothing but the truth." In conse- 
quence the hypothesis is subjected to tests which may 
lead to its confirmation, its rejection, or its modification. 

The two possible modes of verification are recourse to 
experience and appeal to reason ; or empirical proofs and 
rational proofs. In the former the hypothesis is compared 
with facts by means of further observation and experi- 
ment. M. Romanes' experience with the bees is a fair 



444 Logic in the Class Room 

illustration of this form. Possibly the student has already 
noted that Romanes' mode of procedure conforms to the 
"joint method of agreement and difference." In the case 
of rational proofs the hypothesis is subjected to deduct- 
ive demonstration, either of the form of syllogistic argu- 
ment or mathematical calculation. A fair sample of this 
kind of verification is Newton's discovery of universal 
gravitation. When he decided that the moon and the 
apple might be controlled by the same universal force, 
he undertook to establish his hypothesis by mathematical 
calculation. At first his figures seemed to disprove his 
theory, but after a wait of ten years, new data relative 
to the diameter of the earth, removed the apparent dis- 
crepancy. In the case of the discovery of Neptune, the 
verification was both rational and empirical. Mathe- 
matical (rational) calculation led to the assumption that 
the new planet must be at such a point. With this knowl- 
edge the observer was enabled to turn his telescope to the 
spot indicated and there, true to the calculations, was 
Neptune (empirical). 

To summarize: The method of the discoverer involves 
a knowledge of certain fundamental facts; the observa- 
tion of crucial facts; a mental unrest; the constructing 
of an hypothesis through analogy; and finally verifi- 
cation by either appeal to experience, or mathematical 
demonstration. 

6. THE REAL INDUCTIVE METHOD OR DISCOVERER'S 
METHOD NOT IN VOGUE IN CLASS ROOM WORK. 

It has been remarked elsewhere that there are two gen- 
eral mind types, the liberal and the conservative. Also 



Real Inductive Method Not in Vogue 445 

that the natural method of thought animating the former 
k inductive; while the natural method of thought of the 
latter is deductive. The "liberal" is the apostle of new 
truth; the "conservative" an apostle of safe truth. Both 
types are needed ; the one to balance the other. In conse- 
quence both methods are of service in the class room; 
here each should be given its proportionate place. That 
this condition does not obtain may not be apparent, since 
much attention is being given to certain inductive forms, 
such as "proceeding from the concrete to the abstract," 
"from the particular to the general," "from the known to 
the related unknown," etc. Likewise the courses of study 
and the various text books, claim to advocate the use of 
the inductive process. Seemingly these facts point toward 
a very general observance of the inductive tenets. This 
is true with one vital exception : Induction is the natural 
method of the discoverer. With it he acquires knowl- 
edge; but in the class room induction is used to impart 
knowledge. In life the discoverer takes the initiative, 
thinks his own thoughts first hand; but in the school 
room, above the kindergarten, the child is not allowed to 
take the initiative, not even in his play. All is planned 
for him, all doled out, not in the raw, but partially made 
over. The teacher must impart a certain amount of 
knowledge in a given time, and consequently she must 
"set the pace" in this race for second hand facts. To 
allow the child to lead; to give him the benefit of his own 
individuality; to permit him to use the God given spirit 
of discovery which clamors for recognition; would be 
suicidal according to our present standards. If the 



446 Logic in the Class Room 

plan of the discoverer were followed, the course of study 
could not be covered; children would fail of promotion; 
and criticism would be forthcoming from both principal 
and parent. 

In the average class room of the day the inductive 
FORM prevails but the SPIRIT is not in evidence. Like 
a wolf in sheep's clothing induction has entered the class 
room to devour that primal force in the child's make-up, 
which has raised his race above his simian ancestors. Our 
class room methods, being inductive in form but deductive 
in spirit, may train the youngster to be a camp follozver 
but never a leader in thought and action. The call of the 
day is for more initiative ; for more originality ; for more 
individuality; for more enthusiasm. There is too much 
form without the spirit; so much that bespeaks system 
and refinement without those native impulses and native 
abilities which mark one child from another. Like the 
books of a library our children are classified and 
labeled, and when more come in the others are dusted and 
placed on the next higher shelf. How many more cen- 
turies must we wait before the schools will adopt, in spirit 
as well as in form, the pedagogical principles of life? 
Will the time ever come when it may be said that all our 
leaders in thought and action are college graduates ? 

7. AS A METHOD OF INSTRUCTION DEDUCTION IS 
SUPERIOR TO INDUCTION. 

The inductive method is pre-eminently the method of 
the discoverer only when it involves both the form, which 
he follows, and the spirit, which he evinces. The so- 



Deduction is Superior to Induction 447 

called method of the school room is inductive in form, 
as the procedure is from particular facts to general 
truths; but deductive in spirit, as it is used to impart 
knowledge. If it were inductive in spirit, the child would 
be allowed to acquire knowledge entirely through his own 
initiative. Deduction is the method of instruction, 
whereas induction is the method of discovery. That the 
child of the school is instructed or better "deducted" and 
not generally allowed to discover, is a situation so ap- 
parent that we need not labor the point further. 

Because the inductive process has been made a method 
of instruction, it has been robbed of its chief advantage 
over deduction. Indeed, as a method of instruction, 
deduction is really the superior method. It requires less 
time, demands greater concentration, often arouses more 
interest, and creates situations which are less involved. 

8. CONQUEST NOT KNOWLEDGE THE DESIDERATUM. 

In all great inventions, man has taken his cue from 
nature. In inventing the telescope, his model was the 
eye; in building his house, his inspiration was the cave. 
In reality man has accepted nature's suggestions, and 
then attempted to improve upon them. In this he has 
met with success. From the crab apple tree, he has de- 
veloped the northern spy; from the wild hen which laid 
2 5 eggs a year, he has evolved the modern hen which 
produces 225 eggs a year. Moreover, man has attained 
his greatest successes by enlarging upon the thoughts of 
nature and not by unmixed substitutions. Burbank, 
through a long process of years, has changed the color of 



448 Logic in the Class Room 

a flower, but in accomplishing this did he not use some 
hidden tendency of nature? Burbank, with all his wis- 
dom, cannot give a flower color unaided by "Dame 
Nature." 

When man commenced to study nature's mode of edu- 
cation, he saw that fearful sacrifices were entailed, both 
in time and in energy as well as in life itself; and so he 
evolved a more economical way of leading the child 
through the experiences of the race. In consequence, he 
has developed the present splendid system of education. 

In the evolution of all great institutions, there are in 
evidence crucial weaknesses, and in the evolution of man's 
educational system it appears that he has erred in adopt- 
ing nature's form of education without her spirit of edu- 
cation. In his anxiety to have the young acquire as much 
as possible, man has overshot nature's true purpose. For 
example, the big word in man's educational system is 
knowledge ; but the big word in nature's educational sys- 
tem is conquest. Nature gives man knowledge simply to 
reward him for his effort; but man would give to his 
fellow the reward without the effort. According to 
nature, the strongest men are those who overcome most; 
according to man, the strongest men are those who know 
most. The common educational principles, such as, 
"From the concrete to the abstract and from the known 
to the related unknown," etc., are interpreted by man 
from the viewpoint of knozvlcdge; whereas nature would 
teach 'that these are a feasible way to develop power — 
to grow manhood. It is seen that nature uses knowledge 
onlv as a means to an end, and therefore when man uses 



Conquest not Knowledge the Desideratum 449 

knowledge as an end only, he is trying to substitute a plan 
of his own for nature's plan. The best results can be 
secured only when man co-operates zvith nature in de- 
veloping, and at the same time regulating, the spirit of 
conquest. 

9. MOTIVATION AS RELATED TO THE SPIRIT OF DIS- 
COVERY. 

It has been remarked in this chapter, that the "crucial 
fact" serves to stir the mind of the natural born dis- 
coverer to an activity raised to the nth power of effective- 
ness. Naturally, the intent of such activity is to solve the 
mysteries which the crucial fact may suggest. This pas- 
sion of the mind to "know more about it" is appropriately 
termed "the mental urge." From the viewpoint of the 
pedagogue, the "mental urge" is simply an intrinsic inter- 
est in the situation at hand; an interest born of an innate 
or acquired passion to know the truth. 

With the average child, the "mental urge" is strong 
only when the situations appeal to some immediate need 
or vital experience. The attempt to make the school 
work concrete and vital; to make it answer the child's 
natural curiosities and real necessities, is dignified with 
the name "motivation." It is obvious that this is a new 
term for an old condition. To motivate the work, means 
to give to it an attractiveness which any situation might 
have for the true born discoverer and inventor. // we 
would use the discoverer's method successfully, we must 
learn the art of motivating the work. This may be ac- 
complished by appealing to the play instincts, to the busi- 
ness instincts, and to the vital interests of every day life. 



450 Logic in the Class Room 

10. DISCOVERER'S METHOD OR THE REAL INDUCTIVE 

METHOD ADAPTED TO CLASS ROOM WORK. 

A revolt has already set in against this insatiate desire 
to teach knowledge, rather than to teach the child. Many- 
schools are permitting a study of those topics which 
vitally concern every day life. Less attention is being 
given to formal discipline, and more attention to self 
activity. Gradually will the scheme of education be di- 
rected toward fitting the school work to the child, rather 
than fitting the child to the school work. When this new 
thought in education is fully upon us, then will every 
device and method be directed toward giving full scope 
to the spirit of inquiry, which so completely possesses 
every normal child. 

It now remains for us to indicate ways in which the 
spirit of inquiry, or the "discoverer's method," may be 
adapted to school room work. In the first illustration, 
we shall outline the topic as it is generally given in the 
average school where attention is paid to development 
work. This will then be followed by a second outline 
which may be suggestive of the discoverer's mode of 
procedure. 

First illustration. School Room Method. 

I. Aim : To teach addition of business fractions. 

11. Preparation: (Only type examples given). 

(1) (2) (3) 

3 bushels 3 parts Rule: Only like numbers 

-j-5 bushels -)-S parts can be added. 

8 bushels 8 parts 



Discoverer's Method 451 

III. 



Presentation : 








(1) 
3 ninths 
+5 ninths 


(2) 
3/9 

+5/9 


(3) 
2/3= 4/6 
l/6=+l/6 


(4) 
2/3= 8/12 
3/4=+9/12 



8 ninths 8/9 5/6 17/12 

IV. Summary : 

(1) Only like fractions can be added. 

(2) Change unlike fractions to like fractions. 

(3) Add the numerators, placing the sum over 

the common denominator. 

V. Application : 

Examples and problems involving similar and dis- 
similar fractions. 

Before undertaking to illustrate the discoverer's method, 
it may be well to designate in order the evident steps as 
they would appear to the pedagogue : 

( 1 ) Motivate the topic to be presented. 

(2) Bring to mind appropriate "foundation facts/' 

(3) Make evident the "crucial fact." 

(4) Lead to the forming of an hypothesis through 

analogy. 

(5) Afford ample opportunity to prove the hypoth- 

esis. 

Discoverer's Method Adapted. 

Lesson Plan. 

I. Aim : ( 1 ) By playing upon the curiosity or by ex- 
posing a vital need, create a strong desire to know how to 
add business fractions. (Motivate the topic.) 

Curiosity: "We all know what a fraction is and we 
know, too, how to change fractions to higher or lower 



45 2 Logic in the Class Room 

terms." "Now I wonder how many know how to add 
fractions, such as 2/5 and 1/5?" "Don't you tell any 
one, Mary, but just write your answer on a piece of paper 
and show it to me." (Mary's answer shows that she has 
thought correctly, but figured incorrectly. John, after 
having raised his hand, shows his answer to the teacher.) 
"John has the right answer." "That's fine, but let us keep 
the secret, John." "I wonder how many others there are 
in this class who will find the right way?" etc., or 

Vital need : Discuss with the class the various occupa- 
tions of life and secure expressions of preference. Some 
may plan to be real estate agents, others contractors or 
book keepers, etc. "George, you plan to be a book 
keeper." "Let us suppose that I have given you the job 
of book keeper in my factory." "Show that you are 
worth your wages by adding these numbers: 124 3/4, 
647 2/3." "What! can't do it?" "Then I don't want 
you!" etc. 
II. Preparation : 

(2) Bring to the foreground the necessary founda- 
tional knowledge. Suggestions: 

4 bushels 8 parts 

+3 bushels +2 parts 



7 bushels 10 parts 

III. Presentation : 

(3) Make evident the crucial fact. Suggestions: 
Add 2 fifths 3 eighths % 

+ 1 fifth +1 eighth 



3 fifths 4 eighths 



Discoverer's Method 453 

(4) Without further suggestion, give the young dis- 
coverer suitable opportunity for finding the sum of y% 
and y%. In the act of discovering, an implicit hypothesis 
takes form in the mind through analogous reasoning. 
This point marks the climax of the lesson — the supreme 
moment, when the skill and tact of the teacher is assessed 
to the limit. Just here the child must have a comfortable 
environment where perfect concentration is possible. 
Nothing must be forced; and there should be nothing 
suggestive of disgrace or shame, if the youthful Colum- 
bus is unsuccessful. The first attempt should be without 
books. If more help is needed, access to books may be 
given. If the investigation is still without definite result, 
then as a last resort the teacher may, in the presence of 
the child, add fractions, solving with deliberation example 
after example, until the child believes he has discovered 
the process. 

(5) Stimulate a desire to verify the facts discovered. 

Suggestions leading to verification: Afford oppor- 
tunity for mathematical demonstration. Illustrations: 
The fractions >4 and y% have been added in this way — 

y 4 = 2/8 
5/8 

Use is now made of the crucial fact, when the example 
assumes this form — 

2 eighths 
+3 eighths 



5 eighths 



454 Logic in the Class Room 

Or if the class has been trained in the. use of the dia- | 
gram the following may be the form of proof : 



*{ 



H- 



Explanation from diagram. I see that % equals 2 
parts and ^ equals 3 parts; the sum of 3 parts and 2 
parts are 5 parts. But the name of the part is eighths; 
hence the answer 5 parts may be written 5 eighths, or y% 
Thus the final form is 2 parts 
+3 P ar ts 



5 parts=^ 
Give opportunity to consult answers in text books as 
further verification. 

The summary and application of adding fractions ac- 
cording to the "discoverer's method," are virtually the 
same as the corresponding steps in the "school room 
method." 

Second Illustration of Discoverer's Method. 

David P. Page in his Theory and Practice of Teaching 

well illustrates the discoverer's method in conducting a 

general exercise in nature study. We cannot do better 

than to quote from him : 

''It is the purpose of the following remarks to give a specimen 
of the manner of conducting exercises with reference to waking 
up the mind in the school and also in the district. Let us sup- 
pose that the teacher has promised that on the next day, at ten j 



Discoverer's Method 455 

minutes past ten o'clock, he shall request the whole school to give 
their attention five minutes to something that he may have to 
show them. This very announcement will excite an interest both 
in school and at home (playing upon the curiosity) ; and when 
the children come in the morning they will be more wakeful than 
usual till the fixed time arrives. At the precise time, the teacher 
gives the signal agreed upon, and all the pupils drop their studies 
and sit erect. When there is perfect silence and strict attention 
by all, he takes from his pocket an ear of corn and in silence 
holds it up before the school. The children smile, for it is a 
familiar object (foundational knowledge already in hand) ; and 
they probably did not suspect they were to be fed with corn." 

Teacher. "Now, children," addressing himself to the youngest, 
"I am going to ask you only one question about this ear of corn. 
If you can answer it, I shall be very glad. As soon as I ask the 
question, those who are under seven years old, and think they 
can give an answer, may raise their hand. What is this ear of 
corn for?" 

Several of the children raise their hands, and the teacher points 
to one after another in order, and they rise and give their 
answers. 

Mary. It is to feed the geese with. 

John. Yes, and the hens, too, and the pigs. 

Sarah. My father gives corn to the cows. 

Laura. It is good to eat. They shell it from the cobs and send 
it to the mill, and it is ground into meal. They make bread of 
the meal and we eat it. 

"I am sorry to tell you that none of you have mentioned the 
use I was thinking of, though, I confess, I expected it every 
minute. I shall now put the ear of corn in my desk, and no one 
of you must speak to me about it till to-morrow. You may now 
take your studies." 

The consequence of this would be that various families, father, 
mother and older brothers and sisters, would resolve themselves 
into a committee of the whole on the ear of corn : and by the 
next morning several children would have something further to 
communicate on the subject. The hour would this day be 
awaited with great interest and the first signal would produce 
perfect silence. 



456 Logic in the Class Room 

The teacher now takes the ear of corn from the desk and dis- 
plays it before the school; and quite a number of hands are 
instantly raised as if eager to be the first to tell what other use 
they have discovered for it. 

The teacher now says pleasantly, "The use I am thinking of 
you have all observed, I have no doubt; it is a very important 
use, indeed; but as it is a little out of the common course 
(crucial facts) I shall not be surprised if you cannot give it. 
However, you may try." 

"It is good to boil," says little Susan, almost springing from 
the floor as she speaks. "And it is for squirrels to eat," says 
little Samuel. "I saw one carry away a whole mouthful yester- 
day from the cornfield." 

Others still mention other uses. Perhaps, however, none will 
name the one the teacher has in his own mind; he should 
cordially welcome the answer if perchance it is given. (Suppos- 
ing that it has not been given.) "I have told you that the answer 
I was thinking of was a very simple one ; it is something you have 
all observed and you may be a little disappointed when I tell 
you. The use I have been thinking of for the ear of corn is 
this : It is to plant. It is for seed, to propagate that species of 
plant called corn." (Verification.) Here the children may look 
disappointed as much as to say, We knew that before. The 
teacher continues : "And this is a very important use for the 
corn; for if for one year none should be planted, and all the 
ears that grew the year before should be consumed, we should 
have no more corn. The other uses you have named were merely 
secondary. But I mean to make something more of my ear of 
corn. My next question is: Do other plants have seed?" Here 
is a new field of inquiry, etc., etc. 

From the standpoint of "the greatest amount of knowl- 
edge in the shortest possible time," this mode of presenta- 
tion consumes an inexcusable amount of time and is, 
therefore, "impracticable." But when viewed from the 
ground of interest, originality, initiative, and conquest — 
the watchwords of the "new thought in education" ; there 
is no real waste in either time or energy. The spirit and 



Discoverer's Method ' 457 

method of the discoverer will no doubt be the educational 
slogan of the future age. 

Epitome of Discoverer's Method, adapted to the class 
room: 

( 1 ) Motivate the topic to be presented. 

(2) Bring to mind, if necessary, the "foundational 

facts." 

(3) Make evident the "crucial fact." 

(4) Furnish every opportunity for a first-hand dis- 

covery of the "lesson-point" (establishing 
hypothesis through analogy). 

(5) Let the hypothesis be verified. 

The entire situation must be one of freedom, zeal, 
originality, and initiative. 

11. THE QUESTION AND ANSWER METHOD NOT NECES- 
SARILY ONE OF DISCOVERY. 

No one mode of presentation is more universally used 
than the "question and answer." The advantages of this 
mode are many and the teacher who is an adept in the 
art of questioning, from the standpoint of knowledge, is 
generally efficient. The common error, however, incident 
to much questioning, is that of asking "telling questions." 
By the use of such, the class is forced along the desired 
channel of thought so rigorously as to have a condition 
where the spirit of inquiry is entirely wanting. It is pos- 
sible to conform to the rules of good questioning, and 
yet rob the class of all originality and initiative. From 
the teacher's viewpoint, the discoverer's method demands 
few questions ; it is the method of suggestion rather than 



458 Logic in the Class Room 

one of questions. Avowedly in this method, the children 
should ask and answer their own questions. Viewed 
from the ground of discovery there are three modes of 
presentation which may represent a progressive series. 
These are (i) the lecture mode, (2) the question and 
answer mode, (3) the mode by suggestion. In the first 
there is little of the spirit of the discoverer ; in the second 
there is a trifle more of the spirit of the discoverer; while 
in the third there is much of this spirit. The student is 
advised to select some class room topic with a view to 
illustrating these three modes of presentation. 



12. OUTLINE. 


Logic in the Class Room. 


(1) 


Thought is king. 


(2) 


Special functions of induction and deduction. 


(3) 


Two types of mind. 




Inductive or liberal. 




Deductive or conservative. 


(4) 


Too much conservatism in school. 


(5) 


The method of the discoverer. 




Three steps 




( 1. Foundational 
1. Antecedent facts j 2 Crudal 






„ ^ . , i. . ' ( 1. "Mental urge" 
2. Forming hypothesis j 2 Analogy 




„,_.-. C 1. Empirical 
3. Verification j 2 Rational 



(6) The real inductive method or Discoverer's Method not in 
vogue in class room work. 

(7) As a method of instruction, deduction is superior to 
induction. 

(8) Conquest, not knowledge, the desideratum. 



Outline 459 

(9) Motivation as related to the spirit of discovery. 

(10) Discoverer's method or the real inductive method adapted 
to class room work. 

School room method. Discoverer's method. Epitome. 

(11) Question and answer method not necessarily one of dis- 
covery. 

13. SUMMARY. 

(1) Thought is king in that it is the ruling factor in the 
making and breaking of habit. This lends import to logic, which 
is the science of thought. 

(2) The chief function of induction is to discover new truth ; 
whereas deduction aims at clarifying and correcting new truth. 
Inductive logic makes known the special forms of thought which 
the discoverer uses; while deductive logic tends to show how he 
verifies the truth thus obtained. 

(3) Just as there are two general forms of thinking, in- 
ductive and deductive; so there are two general types of mind, 
the inductive and the deductive; the former leads to liberalism, 
the latter to conservatism. Both types are needed to maintain 
a safe balance. 

(4) The schools of the day are emphasizing the deductive 
phase of work to the sacrifice of the inductive. They are 
neglecting the Columbuses and the Edisons of the class. The 
course of study makes for a conservatism, which "nips in the 
bud" any marked tendency to discover and invent. 

(5) Logic may aid in the crusade against the ultra conserva- 
tive tendency of class method, by giving emphasis to the method 
of the discoverer and inventor. An analysis of this method re- 
veals these three steps : antecedent facts, forming an hypothesis 
and verification. Antecedent facts may be divided into founda- 
tional and crucial. A crucial fact leads immediately to the 
formation of the hypothesis; whereas the foundational facts 
represent that body of knowledge which makes it possible to 
interpret the crucial fact. The crucial fact creates an unsatisfied 
state of mind, which, in turn, urges the discoverer to construct 
some satisfactory hypothesis. Inference by analogy is the process 
used in such a construction. The two modes of verification are 



460 Logic in the Class Room 

recourse to experience, or empirical; and appeal to reason, or 
rational. 

(6) In the class room, induction is used in form, not in 
spirit; in consequence we are neglecting the generals for the 
camp followers. 

(7) The inductive method is logically the method of dis- 
covery, while the deductive method is the method of instruction. 
In the class room, both methods have been devoted to the matter 
of instruction. Because of this, induction has been robbed of 
its chief advantage over deduction. 

(8) Man has attained his greatest success by enlarging upon 
the thoughts of nature and not by an absolute substitution. In 
enlarging upon nature's way of educating the child, man has 
adopted her form of procedure, but has lost her spirit of work. 
In his scheme of education, man's watchword is knowledge, 
while nature's is conquest. To seek knowledge without inspiring 
the spirit of conquest is man's way; whereas nature's way is to 
encourage the spirit of conquest by using knowledge as a reward. 
Man must co-operate with nature, if the best results are to be 
secured. 

(9) In the case of the true discoverer, it is not necessary to 
endow the object of his thought with added attractiveness; but 
with the child enthusiasm may need to be stimulated by "moti- 
vating" the subject in hand. This may be accomplished by 
appealing directly to the vital needs, worldly necessities, and f 
innate cravings of the child mind. 

(10) A revolt is in evidence against that insatiate desire to 
teach knowledge, which has been so marked in the past. Already 
schools are introducing departments of work which look toward 
conquest rather than knowledge. 

When adapted to the school room the discoverer's method 
naturally resolves itself into these five steps: 

(1) "Motivate" the topic for presentation. 

(2) Bring to mind "foundational facts." 

(3) Vividly make evident the "crucial fact." 

(4) Lead to discovery of "lesson-point." 

(5) Afford opportunity for verification. 

(11) The question and answer method of presenting work, 



Summary 461 

does not necessarily give full scope to the spirit of inquiry as 
emulated by the true born discoverer. 

As a matter of affording opportunity for the development of 
the spirit of discovery, there are three modes of presentation 
which may be arranged in a progressive series : 

(1) The lecture mode in which there is little opportunity 

for discovery. (2) The question and answer mode 

which permits some opportunity for discovery. 

(3) The mode by suggestion which permits ample 

opportunity for discovery. 

14. REVIEW QUESTIONS. 

(1) Show that thought may be made to make and break habit. 

(2) "Induction directs to new truth, deduction aims to modify 
and correct new truth." Explain and illustrate this. 

(3) Relate radicalism and conservatism to induction and 
deduction. 

(4) Show that in the present day school situations, the spirit 
of deduction prevails. 

(5) Describe a discovery which is a typical illustration of the 
discoverer's method. 

(6) Indicate with explanation the general steps in the dis- 
coverer's method. 

(7) Show by illustration the difference between "founda- 
tional facts" and "crucial facts." 

(8) Explain how the "crucial fact" leads to the construction 
of an hypothesis. 

(9) Explain and illustrate the two ways of verification. 

(10) Distinguish between the inductive method as it is used 
in the class room, and the inductive method as used by the 
discoverer. 

(11) Show that in his inventions, man enlarges upon the 
thoughts of nature. 

(12) Explain "motivation" and show that it is a new name for 
an old situation. 

(13) In adapting the discoverer's method to class work, what 
are the successive steps to be followed? 

(14) Show by illustration that the question and answer method 
is not necessarily one which encourages the spirit of discovery. 



462 Logic in the Class Room 

15. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTI- 
GATION. 

(1) "Our pet thoughts control us." Discuss this. 

(2) Select some class room experience for the purpose of 
showing that induction is especially directive in nature, whereas 
deduction is more or less corrective in nature. 

(3) "There are just two kinds of people in the world, the 
Inductives and the Deductives'' Explain. 

(4) Are the schools sending out too many Deductives? 
Argue the question. 

(5) "It is the business of the teacher to teach himself out of 
the business." Explain. 

(6) Look up the discovery of the laws of the pendulum, with 
a view of showing that the event well illustrates the fact of the 
three general steps in the discoverer's method. 

(7) "With the average, only extraordinary facts become 
crucial; but with the genius any ordinary fact may become 
crucial." Make this clear. 

(8) Explain "mental urge." Illustrate. 

(9) Illustrate "empirical proof," also "rational proof." 

(10) Show by illustration that the inductive method as used 
in the class room, falls far short of being the method of the 
discoverer. 

(11) Indicate by citing historical examples, that conquest 
rather than knowledge makes for manhood. 

(12) Show how you would motivate a topic in geography. 

(13) Outline a plan for teaching some topic in nature accord- 
ing to the discoverer's method. 

(14) Select a topic in arithmetic, for the purpose of giving a 
comparative illustration of the "question and answer mode" of 
presentation, and the "mode by suggestion." 



CHAPTER 21. 

LOGIC AND LIFE. 

1. LOGIC GIVEN A PLACE IN A SECONDARY COURSE. 

"To prepare for complete living" seems to be the ulti- 
mate aim of education, and any school subject which does 
not aid to this end must be eliminated from the courses 
of study. "Knowledge for the sake of knowledge" will 
not do in this age of practical efficiency. A subject in 
order to survive must show indications of doing its share 
in this larger business of man building. If it can be 
made evident that logic lends itself in no undecided terms 
to such an aim, then may its incorporation in a secondary 
course of study be not only justified but more highly 
appreciated. 

2. MAN'S SUPREMACY DUE TO POWER OF THOUGHT. 

That man is the supreme agent of intelligent progress 
is due to three factors : First, to the existence of the nat- 
ural world ; second, to the existence of man himself ; third, 
to man's ability to think. Given life and the world as a 
place to evolve that life, and it is barely possible that man 
might have survived, but without thought he could never 
have become supreme. Man is king of the animal king- 
dom because of his power of thought. Let us illustrate : 

Ages ago when England was a part of the main land ; 
when there was no North Sea nor English Channel ; we 

463 



464 Logic and Life 

are told that there lived in the forest tracts there about b 
many large and ferocious animals ; such as the elephant, 
the lion, and the tiger. There lived also in the region a 
smaller and apparently a weaker animal. This creature 
had no tusks to hook with, no great jaws to crunch with, \ 
and no claws to tear with ; and an eye witness would have 
said "Such a weakling has no possible chance against these | 
enemies of his; he and his descendants will succumb and 1 
the species will become extinct." The region was tropical ; ■ 
but, of a sudden, a cataclysmic twist changed the tern- 1 
perature from a torrid to a frigid state. What happened f 
The large and ferocious animals either migrated to the '■ 
south or froze to death; but this weakling put on furs, j 
built fires, and remained in the jungle as its king. His fe 
name was man, and though he had no horns to hook with, 
he possessed a brain to think with; this gave him suprem- 
acy over the forces of nature. 

From the beginning the adaptation of the lower animals 
has been physical; whereas man's has been more or less 
intellectual. By means of deliberative thought man made \ 
the bow and arrow which could kill at a distance of 200 ^ 
yards; then he invented the repeating rifle which may 
kill a mile away. Thought has taught man to harness 
the forces of nature in the form of all kinds of invention. 
Thought has given man the power to build bridges and 
palaces, to paint pictures, to chisel angels. Thought has 
pierced the fog of ignorance and brought light to the 
dark spots of the globe. Thought has build nations and 
established the spirit of good will on earth. Through the 
long years, thought has been the one tool of conquest 



Man's Supremacy Due to Power of Thought 465 

which has enabled man to build for himself, out of the 
furnishings of nature, a heaven on earth. 

Can you recall a department of life which thought has 
not embellished ? Can you recall a single factor that has 
been raised to the nth power of efficiency without thought? 
Steam and electricity plus thought lights the world, 
unites the world, feeds and clothes the world. To-day, 
as in the olden time, men who think are ever at a pre- 
mium. This holds true from the Shopkeeper to the 
Magnate of Wall Street; from Basil, the Blacksmith, 
to Edison, the King Inventor ; from Reuben, the Farmer, 
to Burbank, the Wizard. 

3. IMPORTANCE OF PROGRESSIVE THOUGHT. 

Man not only thinks but he thinks progressively. The 
average horse of to-day, for example, is probably no more 
intelligent than was the average equine of the time of 
Alexander the Great, whose war horse, Bucephalus, at- 
tained historical fame. Yet, intellectually, the average 
man of to-day is far above the average man of Alex- 
ander's time. "Horse-knowledge" is more or less sta- 
tionary. Through instinct each generation makes use of 
the knowledge of its ancestors without any noticeable 
accretions. But "man-knowledge" is a growing product 
of progressive thought. Man appropriates all the knowl- 
edge of his forbears, and then adds to this a bit of his 
own. By being able to think progressively, man is 
enabled to stand upon the shoulders of his ancestors and 
thus to take advantage of a broader vision. 

We are now led to the conclusion that man's supremacy 



466 Logic and Life 

is due not only to his ability to think, but to his power of 
progressive thought. 

4. NECESSITY OF RIGHT THINKING. 

In the main, man's thinking has been for his good; 
that is, in the long run, it has contributed to his general 
progress. If this had not been so, long since would he have 
dropped back to the level of the non-thinking animals. 

Thinking has been defined as the process of affirming 
or denying connections. Right thinking is, therefore, a 
matter of affirming the right connections or denying the 
wrong connections. To put it differently : right thinking 
is the process of adjusting the best means to a right end; 
whereas wrong thinking is a matter of overlooking the 
best means, or directing improper means to a wrong end. 
Right thinking involves proper adjustment ; wrong think- 
ing improper adjustment. In the intellectual world as in 
the physical, improper adjustment means extinction. 
Illustrations of this : 

(i) A contractor undertakes to build a skyscraper. 
In the excavation an old wall is discovered. The thought 
of the contractor is, "I must make a pot of money out of 
this job, and since this old wall is in the right spot I will 
build on it, and thus save me 'five hundred/ " In the 
course of ten years, without warning, the building top- ■ 
pies over and fifty women and children are killed. The 
contractor is convicted and sent to prison for life. If 
the builder had thought the right thought; namely, "I 
want to put up a building that will stand for generations," 
he would have survived the competition of his fellows and I 



Necessity of Right Thinking 467 

entered his long home with success etched upon his soul. 

(2) Two school teachers, A and B, are working in 
the same system. A's ambition is to be promoted and 
she uses "pull" as the means. For a time she succeeds in 
pulling the wires, and likewise in pulling the "wool" over 
the eyes of the Board of Education. B aspires to pro- 
fessional growth, using as the means every opportunity 
for genuine improvement. In time both are known as 
they really are, not as they seem to be. A is denominated 
a "shirk," a politician, a mere school keeper; whereas B 
is looked up to as the best equipped worker in the 
building, a real school teacher. 

There may seem to be many exceptions to this point of 
view, and yet in the last analysis we find that these ex- 
ceptions are only apparent. When we maintain that 
right thinking means survival and wrong thinking ex- 
tinction, we assume that the standard adopted is genuine 
efficiency and not a certain money basis. High positions 
may be secured through wrong thinking, but these cannot 
be filled creditably without the preponderance of right 
thinking. 

5. INDIFFERENT AND CARELESS THOUGHT. 

It may be advanced as a plausible hypothesis that man, 
especially if he is an American, finds much trouble for 
himself, and makes much trouble for the world because 
of his indifference to thought. To leap first and look 
afterwards is the spirit of youth, and America is young. 
Think twice before you look and look tzvice before you 
leap is sound logical doctrine. A logically minded man 



468 Logic and Life 

rationalizes every new proposition before he adopts it. 
He marshals before the mind the favorable points and 
then bombards them with every conceivable objection. 
With the steady eye of an honest, earnest, open minded 
critic, he weighs the unfavorable against the favorable 
and then accepts the indications of the balance unequiv- 
ocally. If logic did nothing else save to inspire young 
people to thus rationalize every doubtful undertaking, it 
would do its share toward world betterment. 

6. THE RATIONALIZATION OF THE WORLD OF CHANCE. 



Man seems to be a natural born gambler. He loves to 
"take a chance" and herein lies much of his unhappiness. 
Without discussing the evils of the stock exchange, the 
horrors of the gambling den, and the unbusiness like 
procedure of the race track, we may merely attempt here 
to show how the rationalization of the conception of 
chance may be instrumental in dimming the glare of 
gambling to the average youth. 

(i) The meaning of the term chance. 

The term chance implies an inability to find a cause for jl 
any particular event. Whenever we trust to luck, we do 
so through ignorance. In reality every thing in this world 
is ordered according to law, and if we possessed infinite 
knowledge concerning these laws, then, for us, the word 
"chance" would have no meaning. One accomplishment f 
of knowledge has been to rationalize superstition and 
chance. "Not a grain of sand lies upon the beach, but 
infinite knowledge would account for its lying there ; and 
the cause of every falling leaf is guided by the same prin- j: 



The Rationalization of the World of Chance 469 

ciples of mechanics as rule the motions of the heavenly 
bodies." — Jevon's Prin. of Science, vol. I, p. 225. 

That chance is a literal confession of ignorance, is a 
wholesome truth for all to bear in mind. If we were not 
so ignorant of atmospheric conditions, we would never be 
caught in the rain without an umbrella; if we knew per- 
fectly the laws of mechanics, we would not speed our 
car and trust to luck that the car would hold together. 

(2) Chance mathematically considered. 

The principle of the "calculation of chances" has been 
discussed elsewhere. It will be sufficient here to illus- 
trate the principle from a mathematical point of view. 

Suppose that a jeweller desires to dispose of a ten- 
dollar watch by a raffle. He may place a hundred num- 
bers in a box, one of which corresponds to the number 
on the watch. My chance of drawing the right number 
is one out of a hundred and may be expressed by the 

1 

fraction . The fact that I may draw the right num- 

100 

ber on the first trial or on the last trial is immaterial. 

The real meaning of the ratio "one out of a hundred" 

is, that in the long run, I shall lose 99 times where I gain 

but once. This implies, that if I pay 25 cents for each 

draw, I shall in the end pay 99 times 25 cents for the 

watch, or I will have paid $24.75 f° r a ten dollar watch. 

(3) Chance and gambling. 

In all forms of gambling no wealth is produced. What 
one man gains the other man loses. In addition to this 
the institution which projects the gambling scheme must 



470 Logic and Life 

be supported. In consequence, more money must be lost 
than can possibly be gained. This leads to the conclusion 
that on the basis of averages he who would gamble must 
terminate his career "behind the game." Statistics verify 
this conclusion. 

(4) Chance and investments. 

Interest, which is money paid for the use of money, is 
high when the demand for money exceeds the supply and 
low when the supply equals or exceeds the demand. The 
fact that the supply is short is largely due to the lack of 
confidence on the part of the investor. This means that 
he is unwilling to take the risk. Thus the principle: 
"High rate of interest, great risk; lozv rate of interest, 
little risk." 

7. THE RATIONALIZATION OF POLITICAL AND BUSI- 
NESS SOPHISTRIES. 

"Win right or wrong" is a nut shell statement of 
modern sophistry. Corollaries to this are such aphorisms 
as "Of two evils choose the lesser"; "Do evil that good 
may come," etc. Armed with these platitudes the modern 
business and political octopus will play the bully and 
squeeze the life out of the little fellow in the name of 
economy ; will pay for editorials to elect the "right man" ; 
will evade bad laws so-called ; institute lobbies ; buy votes ; 
and perpetrate a thousand other immoral deeds in the 
name of "good business" or of "party loyalty." 

Half truths are the most atrocious of all kinds of 
fallacies in that they are the most misleading. "Do evil 
that good may come" is but half of the whole truth "Do 



The Rationalization of Sophistries 471 

evil that good may come, provided there is no other way 
open." Again, "Of two evils choose the lesser, if a com- 
plete enumeration has shown that there is not a third 
course" 

A development of a finer ability of discernment under 
right influence should lead the common citizen to see 
through these various sophistries practiced by corporate 
greed, and should enable him by means of the ballot to 
"blaze a better way." 

The "public is a blunderbuss" because the average man 
either cannot, or will not, think his own thoughts. By 
developing greater skill and arousing greater interest in 
the thinking process, the crowd of camp followers will be 
reduced; selfish bossism will die; and a truer and more 
efficient democracy will reign supreme. 

8. THE RATIONALIZATION OF THE SPIRIT OF 
PROGRESS. 

Genuine progress comes through a happy combination 
of the old with the new. A love for the old only, means 
ultra conservatism; whereas a love for the new only, 
means ultra radicalism; a love for both means rational 
liberalism. 

That people love the old way may be attributed to two 
forces which will receive attention here. 

(1) Race instinct. 

It may be said that "life is a brief space between two 
eternities — a path between infinity and infinitude." "Man 
is a pedestrian who perambulates along the way." The 
eternities concern him not so much as the path which 



47 2 Logic and Life 

stretches between them. In a former day, one of the 
striking characteristics of the western plain was the 
beaten path stretching out along the table-land like an 
elongated, dust colored serpent; and often following this 
path would be a herd of buffalo winding its way in single 
file around boulder and ant hill till shut from view by the 
distant horizon. Thus has man travelled along the beaten 
path, following the "foot prints of the ages." Here and 
there and everywhere do we see signs of those who have 
gone on before; father, grandfather, great grandfather; 
yes, even to the toe marks of those primeval ancestors of 
ours who shambled along the way, nobody knows how 
many years ago. From the dark recesses of the cave, 
have our forbears thrown a lasso of blood about our 
necks, and it seems as if we must follow the old, old way. 
"Being acorns of the ancestral oak," we grow similar oak 
tree tendencies, living over again the life of our progen- 
itors. "There lies in every soul the history of the 
universe." 

(2) Imitation. 
But there is another reason for this ultra conserva- 
tive spirit and it is that nature's chief mode of instruction 
is by means of imitation. To every living thing of wood 
or field nature seems to say, "Your parents are always 
right, do as they do for this is the best way to learn the 
lessons of life." A man thinks, feels and wills his way 
through life in a certain manner largely because his 
father did likewise. Moreover, we not only imitate those 
who have gone on before, but we counterfeit each other ; 
fashion is another name for world wide mimicry. We 



The Rationalisation of the Spirit of Progress 473 

imitate our friends and those whom we admire; we talk 
like them, we walk like them, we live like them. 

It now appears that we are held to the path of the past 
by means of race instinct and the power of imitation, and 
we are thus prone to believe that the old way is good 
enough. It is evident that to get out of the beaten path 
is dangerous. The wild animal that deserts the habits of 
the race dies a premature death, and the man who pos- 
sesses the temerity to struggle through the thicket of new 
things must, of necessity, shorten his span of life. To 
follow the "same old rut" is easiest for the teacher ; to be 
loyal to the "grand old party" is safest for the politician. 
But to the contrary, if every man of every generation 
had followed the beaten path blindly — without deviation, 
the human race would now be a horde of simians. Be- 
cause man has possessed the power of progressive thought, 
he has developed the spirit of radicalism and has thereby 
made himself supreme. 

"The old way anyway — the old way right or wrong" 
has been the world's biggest stumbling block. Every 
innovation must fight for its life. Every good thing has 
to be condemned in its day and generation. It is Huxley 
who suggests three stages for the course of a new idea : 
First, it is revolutionary ; second, it will make little differ- 
ence; third, / have always believed in it. On the other 
hand, the new way anyway; "we must have a change 
whether or no"; "we must have something different 
despite the cost," have ever been the slogans of waste and 
destitution. The wars which have not resulted from the 
prejudice of ultra conservatism have been brought about 



474 Logic and Life 

through the thoughtlessness of ultra radicalism. The 
revolutionist, the freak and the anarchist, products of 
impulse and the spirit of discontent, spring from an 
unwise love of change. 

The world needs conservatism and radicalism not so 
much as it needs rationalism. It needs men who can 
hold to the good of the old and adopt the best of the new; 
men who neither "rust out" nor "waste out"; but wear 
out. That rational progress may obtain, there must be a 
perfect dovetailing of the old with the new. Man must 
leave the beaten path not altogether, but at times. He 
needs to blaze out a new way not so much as he needs to 
straighten the bends, tunnel through the mountains, and 
fill in the swamps of the old way. A rational "liberal- 
ism" implies a willingness to follow the old path with 
a view to improving the imperfections thereof. 

9. A RATIONALIZATION OF THE ATTITUDE TOWARD 
WORK. 

On the assumption that true happiness is the ultimate 
aim of life, we may conclude that anything which does 
not contribute to this end functions as a curse and not 
as a blessing. Happiness involves physical comfort and 
mental joy. To have comfort of the body implies 
moderate means. The poor cannot be happy because of 
bodily want. When "physical-man" is not given proper 
nourishment for healthy growth, then does he goad 
"spiritual-man" with the pricks of appetite and pain till 
his wants are appeased. This is a law of nature. On the 
other hand happiness is not attained through acquisition; 



A Rationalization of the Attitude Toward Work 475 

neither the millionaires, nor the scholars, nor the famous 
are the happiest. This is a fact apparent to all. Over 
worry and over excitement follow closely the heels of 
much money and high position. Too little brings un- 
happiness through want; too much brings unhappiness 
through worry. Therefore man is cursed by his work 
when the remuneration is not enough for comfort of 
body, or when the income is too much for poise of mind. 
Unless the organs of the body are used they atrophy. 
Every cell of the physical makeup demands exercise. 
Work which is not drudgery; work which causes the 
organs of the body and the powers of the mind to func- 
tion normally ; work which gives comfort without luxury ; 
work which forces one to the highest actualization of his 
physical and spiritual powers is man's greatest blessing. 
In and through such work will man attain his highest 
state of happiness. 

10. THE LOGIC OF SUCCESS. 

We may now hope to show that material aggrandize- 
ment, the adopted standard of success, is one of the 
illogical factors of modern life. 

The tree of the forest always grows toward the light. 
It pushes its way through the darkness of the soil into 
the shadow of the underbrush and finally out into the 
unobstructed light of the sun. This parallels the progress 
of the race. From the darkness of savagery into the 
shadow of barbarism, and finally out into the full light of 
civilization. Thus has man grown steadily and con- 
tinually toward better things. But "better things" is a 



476 Logic and Life 

relative term and has changed with the development of 
the race. "A good healthy idea may not live longer than 
twenty years." In consequence growth toward the light 
has been in accordance with man's conception of a higher 
and a better life; which conception is ever changing. 

Moreover, growth toward the best is always rewarded 
by real happiness. It therefore follows that the right 
road to real happiness extends along the way of better 
things as conceived by the traveller, man. 

Any force which tends to lift the world up toward 
more light is a blessing, and any personality which con- 
tributes to this end is a success. When one drops a pin it 
falls down toward the earth, at the same time the earth 
comes up to meet the pin. This is according to the uni- 
versal law of gravitation. It is true that the earth moves 
the pin through a much greater space than the pin moves 
the earth, and yet the fact remains that the pin does move 
the earth. The extent to which the smaller body is able 
to move the larger, depends on the two factors of weight 
and relative position. If the pin were lighter or farther 
away it would influence the earth so much the less. In 
like manner does the "pin-man" influence the "human- 
world." The extent of this influence is controlled by 
man's weight, or his "lifting power," and the position 
which he occupies; just as the attraction of the pin for 
the earth is controlled by weight and position. 

The facts of history have proved that man's power to 
lift depends not so much upon what he has as upon what 
he is. In short, lifting power is directly in proportion to 
personal worth. Moreover, man's ability to draw human- 



A Rationalization of the Attitude Toward Work 477 

ity up may be increased or decreased by the position 
which he occupies. Such a position must function for the 
best good of the world, and at the same time must elicit 
the highest development of the man. 

To Summarize: 

Individual success involves these three elements : 

First — A man of personal worth. 

Second — A position which draws out the best in the 
man. 

Third — A work which definitely contributes to the 
uplift of the world. 

A definition is now in order : 

Success is the right man in the right place doing his 
best for the highest good of the world. 

11. OUTLINE. 

Logic and Life. 

(1) Logic given a place in a secondary course. 

(2) Man's supremacy due to power of thought 

(3) Importance of progressive thinking. 

(4) Necessity of right thinking. 

(5) Indifferent and careless thought. 

(6) The rationalization of the world of chance. 

(1) Meaning of the term chance. 

(2) Chance mathematically considered. 

(3) Chance and gambling. 

(4) Chance and investments. 

(7) The rationalization of business and political sophistries. 

(8) The rationalization of the spirit of progress. 

(9) A rationalization of the attitude toward work. 

(10) The logic of success. 



478 Logic and Life 

12. SUMMARY. 

(1) To justify its having a place in any course of study, 
logic must lend itself to character building. 

(2) Man is king of the animal kingdom because of his power 
of thought. From the beginning his adaption has been more or 
less intellectual and his chief weapon of conquest has ever been 
his thinking brain. 

(3) Man's supremacy has been due not only to his ability to 
think, but also to his power of progressive thought. 

(4) Right thinking is the process of adjusting the best means 
to a right end. Wrong thinking involves improper adjustment, 
which in turn results in extinction. 

(5) A "logically-minded" man rationalizes every new propo- 
sition before he adopts it. That is, he analyzes with the utmost 
care and with unprejudiced frankness all the favorable and un- 
favorable situations; he then throws them into the balance of 
honest judgment and adopts the indications of said balance, 
unequivocally. 

(6) Chance is a confession of ignorance. If man possessed 
infinite knowledge, the term chance would have no place in his 
vocabulary. 

The games of chance are money making schemes supported 
by the gambling fraternity. On the basis of averages, the gam- 
bler, in the long run, must terminate his career "behind the 
game." 

High rate of interest implies great risk; low rate of interest 
little risk. 

(7) "Win right or wrong" epitomizes the teachings of mod- 
ern sophistry. With the coming of better thinking, a more 
efficient democracy will obtain. 

(8) Rational progress combines the best of the old with what 
seems to be the best of the new. 

Blind love for the old, or ultra conservatism, is due to the two 
forces of race instinct and power of imitation. 

An adherence to the "old way anyway" may mean retrogres- 
sion; whereas following the new way, simply because of its 
newness, may involve unnecessary waste. 



Summary 479 

(9) Work which is not drudgery; work which causes the 
organs of the body and the powers of the mind to function 
normally; work which gives comfort without luxury; work 
which forces one to the highest actualization of his physical 
and spiritual powers is man's greatest blessing. 

(10) Logically considered personal aggrandizement is not a 
true standard of success. Success involves personal worth 
rather than personal holding. 

Success is measured by man's ability to help the world on 
toward better things. 

Success is the right man in the right place doing his best for 
the highest good of the world. 

13. REVIEW QUESTIONS. 

(1) What is the ultimate aim of education?. Show that 
logic contributes to this end. 

(2) Prove that man's power of thought has ever been his 
best weapon of conquest. 

(3) Exemplify the distinction between non-progressive and 
progressive thinking. 

(4) Define right thinking. Illustrate. 

(5) "A logically-minded man rationalizes every new project 
before undertaking it." Give a concrete instance in explanation 
of this. 

(6) "Chance is a literal confession of ignorance." Demon- 
strate this. 

(7) Give a mathematical illustration proving that schemes of 
chance are simply money making devices for the benefit of 
those who project them. 

(8) The average gambler must terminate his career behind 
the game. Prove this. 

(9) Why should high rate of interest imply great risk? 

(10) Show that a half truth is a most misleading fallacy. 

(11) Illustrate a business sophistry. Explain. 

(12) Write a brief theme on "The Rationalization of the 
Spirit of Progress." 



480 Logic and Life 

(13) Under what conditions may work become man's greatest 
blessing? 

(14) Define success. Illustrate. 

(15) In the light of your definition of success discuss the 
following: "The. only failure is not to try." 

14. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- 
TIGATION. 

(1) "To prepare for complete living" is the end of educa- 
tion. Interpret and discuss this quotation from Spencer. 

(2) Mention some discovery or invention which represents 
the power of progressive thought. » 

(3) "Man's adaptation has been largely intellectual while the 
adaptation of the camel has been physical." Explain. 

(4) Interpret the expression, "The son stands upon the 
shoulders of the father." 

(5) Illustrate instances where man's thinking has not been 
for his best interests. 

(6) Indicate how wrong thinking led to the Civil War. 

(7) Distinguish between legitimate speculation and gambling. 

(8) Name and explain the logical elements involved in a 
low rate of interest. 

(9) How may training in right thinking lead to more efficient 
citizenship ? 

(10) "There lies in every soul a history of the universe/' 
Show the truth of this. 

(11) Show by illustration that imitation is one of nature's 
chief modes of instruction. 

(12) Explain the meaning of drudgery. 

(13) Mention instances where work is a curse. 

(14) Is success possible when the right man is found doing 
his best in the wrong place? 

(15) Whom do you consider the most successful American? 
Give reasons. 



General Exercises 481 



GENERAL EXERCISES IN TESTING THE VALIDITY OF 
CATEGORICAL ARGUMENTS. 

Let the student give attention to the fallacies in meaning as 
well as to the fallacies in form. 

1. None but those who are contented with their lot in life 
can justly be considered happy. But the truly wise man will 
always make himself contented with his lot in life, and, therefore 
he may justly be considered happy. Keynes. 

2. Suffering is a title to an excellent inheritance; for God 
chastens every son whom he receives. Keynes. 

3. No young man is wise; for only experience can give 
wisdom, and experience comes only with age. Keynes. 

4. Dr. Johnson remarked that "a man who sold a penknife 
was not necessarily an 'iron-monger." Against what logical 
fallacy was this remark directed? Explain. Keynes. 

5. This pamphlet contains seditious doctrines, the spread of 
which may be dangerous to the state; hence the pamphlet must 
be suppressed. Keynes. 

6. Good workmen do not complain of their tools: my pupils 
do not complain of their tools; therefore, my pupils are probably 
good workmen. Keynes. 

7. Knowledge gives power; consequently, ,since power is de- 
sirable, knowledge is desirable. Keynes. 

8. Some who are truly wise are not learned; but the virtuous 
alone are truly wise; the learned, therefore, are not always 
virtuous. Keynes. 

9. The spread of education among the lower orders will make 
them unfit for their work; for it has always had that effect on 
those among them who happen to have acquired it in previous 
times. Keynes. 

10. Slavery is a natural institution and therefore ought not 
to be abolished. Russell. 

11. The yardstick of success is the dollar, and you have made 
your millions. 



482 General Exercises 

12. "All who talk well are not necessarily intelligent, and A is 
certainly a spell-binder." 

13. Gold and silver are the wealth of a country; consequently, 
the diminution of gold and silver by exportation must mean the 
diminution of the wealth of a country. Russell. 

14. A miracle is unbelievable, because it fails to conform to 
known laws of nature. 

15. Improbable events happen every day; now, what happens 
every day is a probable event; therefore, improbable events are 
probable events. 

16. What fallacy did Columbus commit when he made the egg 
stand on end by breaking one end? 

17. Some holder of a ticket is sure to draw the prize; and, 
as I am a ticket holder, I am sure to draw the prize. Russell. 

18. All the members of the jury are just men, hence you may 
trust the foreman. 

19. Select the star players of the country and you will have a 
team which cannot be beaten. 

20. All the houses on this street present a pretty picture; this 
house, therefore, which is on this street, will make a fine picture. 

21. What is the good of all your teaching, for every day we 
hear of wrong doing made possible by education. 

22. You are not what I am; I am a teacher; hence you are 
not a teacher. 

23. The student of history is compelled to admit the law of 
progress, for he finds that society has never stood still. Russell. 

24. This bill must have been designed to bleed the people be- 
cause it is supported by the grafters of the state. 

25. "To close the saloons on Sunday is contrary to the wishes 
of the people of the city; hence those 'farmer legislators' should 
keep hands off." 

26. Success is the right man in the right place doing his best, 
and you are working to the limit. 

27. Early to bed and early to rise, makes one healthy, wealthy 
and wise. It is, therefore, easy enough to get rich. 

28. Honesty being the best policy, I must tell the truth to my 



General Exercises 483 

patient, though to tell him that he cannot live will shorten his 
life many days. 

29. A stitch in times saves nine, hence an ounce of prevention 
is worth a pound of cure. 

30. The richest man I know used to sweep his office every 
morning, hence it pays to commence at the bottom. 

31. Cramming is an injurious habit, since it makes the building 
of logical memories practically impossible. 

32. A strong will means a trained will ; struggle is an indication 
of weakness. 

33. There is no such thing as a national or state conscience; 
therefore, no judgments can fall upon a sinful nation. Hibben. 

34. The principles of justice are variable; the appointments of 
nature are invariable; therefore, the principles of justice are no 
appointment of nature. Aristotle. 

35. Intelligence and not sex should be the standard; therefore, 
let the women have their way. 

36. "War by killing off the men of the country gives the living 
a better opportunity to succeed because of reduced competition." 

37. Since you deem yourself a misfit, in the name of common 
sense, why do you not change your occupation? 

38. The conquest of America by Europeans has been a good 
thing for the world; since no eminent historian doubts it. 



484 General Exercises 



GENERAL EXERCISES IN TESTING THE VALIDITY OF 

HYPOTHETICAL, DISJUNCTIVE AND 

DILEMMATIC ARGUMENTS. 

The student must remember to give attention to the fallacies 
in meaning as well as to the fallacies in form. 

1. If I speak at length, he is bored; if I speak briefly, he is 
offended; therefore I will not speak at all. 

2. If virtue is involuntary, vice is also involuntary, but vice 
is voluntary, hence virtue is also. 

3. If a man cannot make progress toward perfection, he must 
either be a brute or a divinity; but no man is either; therefore 
every man is capable of such progress. Fowler. 

4. If education is popular, compulsion is unnecessary; if 
unpopular, compulsion will not be tolerated. Fowler. 

5. If you are to recover from this illness, then you will. If 
you are not to recover, then you will not, hence what is the use 
of calling in a physician? 

6. If your act was right, your conscience will approve it; if 
wrong, your conscience will prick you. Either your act was 
right or wrong, so you can depend upon your conscience. 

7. If he is intoxicated then he is not responsible but he acts 
like a sober man. 

8. If the Elixir of Life is of any value, those who take it 
will improve in health; now my friend who has been taking 
it has improved in health, and therefore the elixir is of value 
as a curative agent. Hyslop. 

9. If you will settle down to business, you may still win out, 
because I am confident it is not too late for hard work to be 
effective. 

10. If the end justifies the means then money used for any 
object of charity may be secured in any way. 

11. If might is right then money talks, but I find that occa- 
sionally money proves ineffective. 

12. If the majority of those who use public houses are pre- 



! General Exercises 485 

pared to close them, legislation is unnecessary, but if they are 
not prepared for such a measure, then to force it on them by 
outside pressure is both dangerous and unjust. Hyslop. 

13. If the conscience is infallible in matters of right and 
wrong, then sin is just one thing; namely, doing that which is 
contrary to one's conscience. We believe that an educated 
conscience is infallible. 

14. If the earth were of equal density throughout, it would 
be about 2 l / 2 times as dense as water; but it is about S l / 2 times 
as dense; therefore the earth must be of unequal density. 
Hyslop. 

15. The end of human life is either perfection or happiness; 
death is the end of human life, therefore death is either perfec- 
tion or happiness. Creighton. 

16. That chauffeur either lost his head or was drunk because 
no sane man would deliberately run down an innocent child. 

17. If you argue on a subject which you do not understand, 
you will prove yourself a fool; for this is a mistake which fools 
always make. Keynes. 

18. If you are a man of your word, you will live up to your 
agreement, or if you have any self respect, you will do the 
manly thing. Now your neighbors tell me that you are a man 
in the habit of making good your promises. 



486 Examination Questions 



SETS OF EXAMINATION QUESTIONS FOR TRAINING 
SCHOOLS AND COLLEGES. 

Answer ten questions. Time, 2 hours. 

Set I. 

1. 

Define and illustrate obversion and state the principle which 
conditions the process. 

2. 
Give directions for making the following propositions logical: 

(1) Only first class passengers may ride in parlor cars. 

(2) All who claim to be pious are not pious. 

(3) "Blessed are the merciful." 

3. 

Write a theme of 200 words on "Logic and Life." 

4. 

Put into syllogistic form and test the validity of this argument. 
"We are going to have an open winter because the hornets' nests 
are near the ground." 

5. 
Justify the teaching of logic in an institution which offers 
courses in Educational Theory. 

6. 
Correct the following definitions, stating the rules violated: 

(1) A man is an organized entity whose cognitive powers 

function rationally. 

(2) A bird is an animal that flies. 

(3) A scholar is an educated man with scholarly attain- 

ments. 

7. 

Prove that in the first figure the minor premise must be affirma- 
tive. 

8. 

Investigate a case of habitual tardiness by making use of the 
canon of difference. 



Examination Questions 487 

9. 

Describe with illustrations the various ways of begging the 
question. 

10. 

Why should classification rather than logical division be the 
mode of procedure in the case of small children? Illustrate. 

11. 

Illustrate the following: (1) non connotative- term, (2) un- 
distributed middle, (3) fallacy of accident. 

Set II. 
Answer ten questions. Time, 2 hours. 

Throw the following into the form of a syllogism and criti- 
cise, giving reasons: 

1. 

"I do not know how to teach school as I have had no 
experience." 

2. 
"Only the honest should be in business and you are not honest." 

3. 

Why should all teachers study logic? Give arguments in full. 

4. 

Describe Mill's methods of induction and illustrate one. 

5. 
Give and explain the rules of logical definition. 

6. 

Explain the distribution of terms and illustrate by circles the 
meaning of the four logical propositions. 

7. 

Define the following: (1) teaching, (2) extension of terms, 
(3) obversion, (4) hypothesis, (5) relative term. 

8. 
Give a class room illustration of the Complete Method. 



488 Examination Questions 



Distinguish between (1) distributive and collective terms, (2) 
analysis and deduction, (3) logical division and classification. 

10. 

Illustrate the following: (1) contradictory proposition, (2) 
analogy, (3) law of identity, (4) singular term, (5) univocal 
term. 

11. 

Convert, if possible, the following: 

(1) Some men are honest. 

(2) All that glitters is not gold. 

(3) All kings are fallible. 

Set III. 

Time, 2 hours. 
1. 

Investigate by the Joint Method of Induction this question : 
"Why is John absent so often?" 

2. 

Explain and illustrate: (1 contradictory propositions, (2) 
illicit middle, (3) obversion, (4) contraversion, (5) synthesis. 

3. 

State and exemplify the rules of logical division. 

4. 

Write a theme of at least 150 words on one of the following: 
(1) Induction as the Discoverer's Method. (2) A Rational View 
of Success. 

5. 
Define logically: (1) teaching, (2) deduction, (3) education, 
(4) analysis, (5) money. 

6. 
Distinguish between the extension and intension of terms. 

7. 

Exemplify: (1) an absolute term, (2) the complete method, 
(3) non connotative terms, (4) fallacy of accident, (5) hy- 
pothesis. 



Examination Questions 489 

8. 
"Educated among savages, he could not be expected to know 
the customs of polite society." Is this valid? Reasons. 

9. 

The signs indicate that you are either stupid or unprepared; 
but the past proves that you are not the former." Test the 
validity. 

10. 

Discuss comprehensively one of the following topics: (1) 
The Fallacies. (2) Thinking. (3) Abbreviated Arguments. 

Set IV. 
Answer ten questions. Time, 2 hours. 

1. 
Exemplify: (1) the law of variation in the extension and 
intension of terms, (2) a distributed predicate. 

2. 

Indicate with explanation the logical errors: (1) A teacher 
assumes that the "bad boy of the school" is going to cause 
trouble in her room. (2) All the men of the Commission are 
fair minded men, hence they will render a fair decision. 

3. 

What experimental method of induction is the most positive 
in its conclusion? Illustrate this method. 

4. 

State and illustrate the rules of logical definition. 

5. 

Obvert each of the four logical propositions. Explain the 
principle involved. 
Test the validity of the following arguments : 

6. 

"Horses, not being human, cannot reason." 

7. 

"Only the industrious deserve to succeed and you have never 
done a hard day's work in your life." 

8. 
"If you had been wise, you would have refused to stoop to 
the methods of the firm, but you were not wise." 



490 Examination Questions 

9. 
From this premise construct a valid syllogism: "All large 
cities owe their size to some commercial advantage." 

10. 
Define and illustrate the following: analogy, hypothesis, think- 
ing, connotative term, relative term. 

11. 

Distinguish between: (1) Analysis and deduction. (2) Logical 
division and classification. (3) Relative and absolute identity. 

Set V. 

Time, 2 hours. 
Test the validity, giving reasons : 

1. 

All successful teachers are industrious, but you are not indus- 
trious because you are not successful. 

2. 

John was a troublesome boy in the first and second grades, 
therefore he is going to make trouble for the third grade teacher. 

3. 

Teaching is the art of imparting knowledge. Criticise, giving 
reasons. Define correctly, pointing out the essentials. 

4. 

Explain the extensional and intensional use of terms and illus- 
trate the law of variation. 

5. 
Describe Mill's experimental methods of induction. Symbolize 
the joint method. 

G. 
Define the following: analysis, law of identity, obversion. 

7. 

Illustrate the laws of thought. 

8. 
Write on one of the following topics: (1) Complete Method, 
(2) Right Thinking. 

9. 
"The science of logic never made a man reason rightly." Dis- 
cuss this question. 



Examination Questions 491 

10. 

Explain and illustrate the enthymeme. 

Set VI. 

Answer ten questions. Time, 2 hours. 

1. 
Exemplify the following: (1) illicit minor, (2) begging the 
question, (3) law of excluded middle, (4) inductive method. 

2. 

Write a short theme on one of these topics: (1) Thinking. 
(2) Logical Terms. 
Test the validity of the "attending arguments, giving reasons : 

3. 

"He who talks much usually says little and you are certainly a 
great talker." 

4. 
"You must be industrious, since only such truly succeed." 

5. 

Illustrate and give the characteristic marks of the joint method 
of induction. 

6. 
Summarize the benefits to be derived from a study of logic. 

7. 

State and illustrate the rules of logical definition. 

8. 
Distinguish between (1) extension and intension, (2) opposite 
and contradictory terms, (3) analysis and synthesis. 

9. 

Define and illustrate hypothesis, obversion, sorites, hypothetical 
argument. 

10. 
Explain and illustrate the three forms of induction. 

11. 
Distinguish logically between a teacher and an instructor. 



492 Bibliography 



BIBLIOGRAPHY. 

Aikins. The Principles of Logic. Henry Holt and Co., New 

York. 1905. 
Bain. Logic, Inductive and Deductive. Longmans, Green and 

Co. 1902. 
Bosanquet. The Essentials of Logic. The MacMillan Co., 

London. 1910. 
Bradley. The Principles of Logic. London. 1886. 
Creighton. Introductory Logic. The MacMillan Co., New 

York. 1905. 
Dewey. Studies in Logical Theory. The University of Chicago 

Press. 1903. 
Fowler. The Elements of Deductive and Inductive Logic. 

Oxford. 1905. 
Hibben. Logic, Deductive and Inductive. Chas. Scribner's Sons, 

New York. 1906. 
Hyslop. Elements of Logic. Chas. Scribner's Sons, New York. 

1905. 
Jevons-Hill. Elements of Logic. American Book Co., New 

York. 1883. 
Keynes. Formal Logic. The MacMillan Co., London. 1906. 
Lotze. Logic. Translated by B. Bosanquet, 2 vols. Oxford. 

1888. 
McCosh. Laws of Discursive Thought. Chas. Scribner's Sons. 

1906. 
Mill. A System of Logic, 2 vols. Longmans, Green and Co., 

London. 1904. 
Russell. Elementary Logic. The MacMillan Co., New York. 

1908. 
Ryland. Logic. George Bell and Sons, London. 1900. 
Sigwart. Logic. Translated by Helen Dendy, 2 vols. The 

MacMillan Co. 1895. 
Swinburne. Picture Logic. Longmans, Green and Co., London. 

1904. 
Taylor. Elementary Logic. Chas. Scribner's Sons, New York. 

1911. 
Venn. The Logic of Chance. The MacMillan Co., New York. 



Outline of Briefer Course 



493 



OUTLINE OF BRIEFER COURSE. 

Subject. Page 

I. THOUGHT AND ITS LAWS 

Logic Defined 3 

The Thinking Process . . . .12 

Stages in Thinking 25 

Law of Identity 32 

Law of Contradiction 35 

Law of Excluded Middle . . . -39 

II. LOGICAL TERMS 

All of Chapter 4 47 

III. EXTENSION AND INTENSION OF TERMS 

All of Chapter 5 62 

IV. DEFINITION 

All of Chapter 6 . • JJ 

V. LOGICAL DIVISION AND CLASSIFICATION 

All of Chapter 7 105 



VI. LOGICAL PROPOSITIONS 

All of Chapter 8 Except Section 7 . . 120 

VII. IMMEDIATE INFERENCE 

All of Chapter 10 170 

VIII. MEDIATE INFERENCE 

All of Chapter 11 Except Section 8 . . 192 



494 Outline of Briefer Course 

Subject. Page 

IX. FIGURES AND MOODS 

The Four Figures of the Syllogism . . 218 

The Moods of the Syllogism . . .221 

Testing the Validity of the Moods . . 223 

X. INCOMPLETE SYLLOGISMS 

Enthymeme 247 

Polysyllogisms 250 

Sorites 251 

XI. CATEGORICAL ARGUMENTS TESTED 

All of Chapter 14 263 

XII. HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS 
All of Chapter 15 Except Sections 13, 14, 

15 and 17 ....... 288 

XIII. THE LOGICAL FALLACIES 

All of Chapter 16 . . . . . 322 

XIV. INDUCTIVE REASONING 

All of Chapter 17 Except Sections 3, 4., 7, 

8 and 9 355 

XV. MILL'S METHODS OF OBSERVATION AND 
EXPERIMENT 

All of Chapter 18 386 

XVI. OBSERVATION, EXPERIMENT AND HYPOTHESIS 
All of Chapter 19 418 



INDEX 



Absolute Terms, 56. 

Abstract Terms, 51. 

Accent, Fallacy of, 330. 

Accident, 81 ; Fallacy of, 334. 

Affirmative Proposition, 127. 

Agreement, Method of, 387. 

All — not, Some, Few, Logical 
Significance of, 133. 

Ambiguous Middle, 328. 

Amphibology, 329. 

Analogy, 368. 

Analysis, Definition of, 97; As 
a Method, 97; Induction by, 
373. 

Analytic Propositions, 138; 
Method, 97. 

Antecedent, 289. 

Apprehension and Thinking, 
24. 

Arguments, Irregular, 258; 
Testing of Categorical, 263 ; 
Incomplete, 247; General Ex- 
ercises, 481 ; Mistakes of Stu- 
dents in Connection with, 
281; Hypothetical, 288; Dis- 
junctive, 302; Dilemmatic, 
308. 

Argumentum ad populum, 338; 
ad hominem, 338; ad igno- 
rantiam, 338; ad baculum, 
338; ad verecundiam, 339. 

Aristotle's Dictum, 208. 

Art, Definition of, 96. 

Auxiliary Elements of Induc- 
tion, 418. 

B 

Bain Quoted, 12. 

Ballentine Quoted, 359. 

Barbara, Celarent, etc., 234. 

Begging the Question, 341. 

Bibliography, 492. 

Bowen Quoted, 12. 

Briefer Course, Outline of, 493. 



Canons of Syllogism, 209; of 
Four Figures, 226. 

Categorematic Words, 48. 

Categorical Arguments, 263 ; 
Tested, 263; General Exer- 
cises, 481. 

Categorical Propositions De- 
fined, 121 ; Four Elements, 
122; Four Kinds, 126; Classi- 
fication of, 128. 

Cause, Fallacy of False, 340. 

Chance, Rationalization of, 468. 

Child, Thinking of, 20. 

Circulus in Probando, 343. 

Classification Compared with 
Division, 112; Kinds, 113; 
Rules of, 114; Use, 114. 

Co-extensive Propositions, 142. 

Collective Terms, 50. 

Comparison, Stages in Think- 
ing, 25. 

Complete Method, Three Ele- 
ments, 97. 

Composition, Fallacy of, 331. 

Concept, Definition of, 17; a 
Thought Product, 21. 

Concomitant Variations, 402. 

Concrete Terms, 51. 

Connotative Terms, Two-fold 
Function of, 62; Definition 
of, 52 ; a List of, 65. 

Conquest the Desideratum, 447. 

Consequent, 289; Fallacy of 
False, 339. 

Contradiction, Law of, 35. 

Contradictory Terms, 53 ; Prop- 
ositions, 167. 

Contrary Propositions, 165. 

Contraversion, 181 ; Fallacies 
of, 327. 

Converse Accident, Fallacy of, 
335. 

Conversion, 176; by Limitation, 
178; Simply, 179; Fallacies 
of, 327. 



496 



Index 



Copula, 123. 

Creighton Quoted, 4, 387, 485. 

D 

Deduction, Denned, 96; as a 
Method, 97; Special Func- 
tion of, 438. 

Definition, Importance of, 77; 
the Predicates, 77; Nature 
of, 82; Definition of, 83; 
Compared with Division, 84; 
Kinds of, 85; When Service- 
able, 87; Rules of. 88; Terms 
which Cannot be Defined, 93 ; 
of Common Educational 
Terms, 94. 

Denomination, Stages in 
Thought, 26. 

Denotation and Connotation of 
Terms, 66. 

Descriptive Definition, 86. 

Development, Definition of, 94. 

Dichotomy, 110. 

Difference, Method of, 393. 

Differentia, 80. 

Dilemma, 308. 

Discoverer's Method, 440. 

Disjunctive Arguments, 302; 
Rules of, 303; Logical Dis- 
junction, 303; Reduction of, 
307. 

Distribution of Subject and 
Predicate of Propositions, 
145 ; Schemes for Remember- 
ing, 148. 

Division, Definition of Logical, 
105; As Partition, 107; Com- 
pared with Definition, 84 
Distinguished from Enu 
meration, 106; Rules of, 108 
Compared with Classifica 
tion, 112; Use of, 114 
Fallacy of, 332. 

Dressier Quoted, 12. 



Education, Defined, 94; Com- 
pared with Instruction, 95. 
Educational Terms Defined, 94. 



Elements of the Logical Prop- 
osition, 123. 

Elliptical Propositions, 129. 

Enthymeme, 247. 

Epicheirema, 249. 

Episyllogism, 250. 

Epithets, Question Begging, 
343. 

Essential Attributes of Defini- 
tion, 88. 

Etymological Definition, 85. 

Euler's Diagrams, 141. 

Evolution and the Thinking 
Mind, 19. 

Examination Questions, 486. 

Exceptive Propositions, 135. 

Excluded Middle, Law of, 39. 

Exclusive Propositions, 136. 

Exercises, Testing Arguments, 
481. 

Experiment as an Element in 
Induction, 419. 

Extension and Intension of 
Terms, Defined, 63 ; Com- 
pared, 63; Used in Compari- 
son, 65 ; Other Forms of Ex- 
pression for, 66; Law of 

Variation in, 66. 



Fact, Defined, 96. 

Fallacies, of Deductive Reason- 
ing, 322; Paralogism and 
Sophism, 322; Division of, 
323; of Immediate Infer- 
ence, 326; in Form, 194, 199; 
Hypothetical, 291; Disjunc- 
tive, 303; of Language, 328; 
in Thought, 334. 

False Cause, 340. 

False Consequent, Fallacy of, 
339. 

Figure of Speech, Fallacy of, 
333. 

Figures of Syllogism, 218; 
Special Canons of, 226; Per- 
fect and Imperfect, 235 ; Re- 
duction, 235; Relative Value 
of, 239. 



Index 



497 



Formal Fallacies, 197, 324. 
Four Terms, Fallacy of, 329. 
Fowler Quoted, 4, 360. 
Fundamentum Divisionis, 108. 



General Exercises in Testing 
Arguments, 481. 

General Terms, 49. 

Genus and Species, 78. 

Grammatical Subject and Pred- 
icate, 125. 

Grammatical Sentences, 131. 



H 

Hamilton Quoted, 4, 12, 131. 

Hibben Quoted, 4, 441. 

Huxley Quoted, 473. 

Hypothetical Arguments, 288; 
Kinds, 290; Rules and Falla- 
cies, 291 ; Reduced to Cate- 
gorical, 293; Illustrative Ex- 
ercise in Testing, 297; Gen- 
eral Exercises, 484. 

Hypothesis, Defined, 96, 425; 
and Theory, 427; Require- 
ments of, 427; Uses of, 429. 



Identity, Law of, 32; Absolute, 
33; Complete and Incom- 
plete, 33; Relative, 34. 

Illicit Major and Minor, 199; 
Illustration of, 215. 

Image, Definition of, 17. 

Immediate Inference, 159; by 
Obversion, 170; by Opposi- 
tion, 161 ; by Conversion, 
176 ; t by Contraversion, 181 ; 
Epitome of Four Processes, 
182 ; by Inversion, 183 ; Falla- 
cies of, 326. 

Imperfect Induction, 361. 

Indefinite Propositions, 129. 

Individual Proposition, Nature 
of, 132; in Opposition, 168. 



Induction, Defined, 96; as a 
Method, 97; Reasoning, 355; 
and the Hazard, 356; the 
Three Forms of, 365; Per- 
fect, 375; Special Function 
of, 438. 

Inference, Definition of, 18; a 
Thought Product, 24; Imme- 
diate, 159; Mediate, 192. 

Infima Species, 79. 

Instruction Defined, 95. 

Intension of Terms, 63. 

Integration, a Stage in Thought, 
26. 

Inversion, 183. 

Inverted Proposition, 137. 

Irregular Arguments, 258. 

Irrelevant Conclusion, 337. 



Jevons Quoted, 4, 25, 387, 468. 
Joint Method of Agreement 

and Difference, 397. 
Judgment, Definition of, 17; a 

Thought Product, 22; Most 

Fundamental Element in 

Thinking, 23. 



K 



Keynes Quoted, 481, 485. 

Kinds of Definitions, 85. 

Knowing, by Intuition and by 
Thinking, 2; Knowing and 
Thinking Compared, 10; by 
Intuition, 11; Habitual, 11. 

Knowledge, Defined, 95; Intui- 
tive, 11. 



Language and Thought Insep- 
arable, 47. 

Law of Variation in Exten- 
sion and Intension, Stated, 
66; Two Important Facts in, 
69 ; Diagrammatically Illus- 
trated, 70, 71. 



498 



Index 



Laws of Sufficient Reason, 40; 
of Universal Causation, 361 ; 
of Uniformity of Nature, 
362. 

Laws of Thought, 32 ; Unity of, 
40; Schematic Statement of, 
43. 

Learning, Defined, 95. 

Logic, Defined, 3; Authentic 
Definitions of, 4; Grammai 
of Thought, 3; Science of 
Sciences, 3; the Value of to 
the Student, 5; Related to 
Other Subjects, 1; Specific 
Scope, 2. 

Logic in the Class Room, 437. 

Logic and Life, 463. 

Logic of Success, 475. 

Logical Definition, 85, 88. 

Logical Disjunction, 303. 

Logical Subject and Predicate, 
125. 

M 

Major Term, 196. 

Material Fallacies, 323, 324, 

325, 328. 
Mediate Inference, 192; the 

Syllogism, 192; Rules of 

Syllogism, 193. 
Method Defined, 96; Inductive 

and Deductive, 97; Complete, 

97. 
Method- Whole Defined, 96. 
Middle Term, 192, 193, 196. 
Mill Quoted, 5, 359, 361, 387, 

393, 397, 402, 406. 
Mill's Experimental Methods, 

386. 
Miller Quoted, 12. 
Mind, the Unity of, 1 ; Know- 
ing and Thinking Compared, 

10. 
Minor Term, 196. 
Mnemonic Lines, 234. 
Modal Proposition, 139. 
Modus Ponendo Tollens, etc., 

302. 



Moods of Syllogism, 221 ; Test- 
ing Validity of, 223. 

Motivation as Related to Spirit 
of Discovery, 449. 
N 

Negative Proposition, 127. 

Negative Terms, 53. 

Nego-positive Terms, 55. 

Non-connotative Terms, 52. 

Non Sequitur, Fallacy of, 339. 

Not, Bisects the World, 36; 
Two Uses of, 36. 

Notion, Definition, 14; Indi- 
vidual, 14; General, 14; Dis- 
tinguished from Knowledge, 
15; Distinguished from Idea, 
16; Psychological Terms In- 
volved in, 16. 
O 

Observation, 419; Rules of, 
420; Errors of, 423. 

Obversion, Definition of, 170; 
Fallacies of, 326. 

Opposite Terms, 53. 

Opposition, Nature of, 161; 
Scheme of, 163; Square of, 
164. 

Outline of Briefer Course, 493. 
P 

Page Quoted, 453. 

Particular Propositions, 126; 
Affirmative, 143 ; Negative, 
144. 

Partition, 107. 

Partitive Propositions, 133. 

Percept, Definition of. 17; Re- 
lated to Thought, 18. 

Perfect Induction, 375. 

Petitio Principii, 341. 

Plurative Propositions, 132. 

Polysyllogism, 250. 

Pornhyry, Tree of, 111. 

Positive Terms, 53. 

Predicables. Defined, 77; 
Named, 78; Illustrated, 82. 

Predicate, Grammatical and 
Logical, 125; Distribution of, 
145. 



Index 



499 



Primary Laws of Thought, 32. 
Privative Terms, 55. 
Progressive Thought, 465. 
Property, 81. 

Propositions, Definition of Log- 
ical, 120. 
Prosyllogism, 250. 
Proximate Genus, 79. 
Pure Proposition, 139. 

Q 

Quantity Signs, 123. 

Quantity and Quality of Prop- 
ositions, 126. 

Question and Answer, not a 
Method of Discovery, 457. 

Question Begging Epithets, 343. 

Question, Complex, 340. 

R 

Rationalization, of Chance, 468 ; 
of Political and Business 
Sophistries, 470 ; of the Spirit 
of Progress, 471 ; of the At- 
titude toward Work, 474. 

Reasoning, Defined, 24, 355; 
Inductive, 355 ; Deductive, 
355. 

Reduction of Figures, 235. 

Relation between Subject and 
Predicate, 140. 

Relative Terms, 56 

Residues, Method of, 406. 

Right Thinking, 466. 

Rules, of Logical Definition, 
88; of Logical Division, 108; 
of Classification, 114; of the 
Syllogism, 193; of the Hy- 
pothetical Argument, 291; of 
the Disjunctive, 303. 

Russell Quoted, 481, 482. 

Ryland Quoted, 481, 482. 



Salisbury Quoted, 360. 
Science, Defined, 95. 
Sensation, Defined, 17; Re- 
lated to Thought, 18. 
Simple Conversion, 179. 



Simple Enumeration, 367. 

Singular Terms, 49. 

Socrates, 322. 

Sorites, 251. 

Species, 78. 

Square of Opposition, 164. 

Subaltern Propositions, 164. 

Subcontrary Propositions, 164. 

Subject, Logical, 123; Gram- 
matical and Logical Dis- 
tinguished, 125; Distribution 
of, 145. 

Success, Logic of, 475. 

Sufficient Reason, Law of, 40. 

Summum Genus, 79. 

Syllogism, a Product of In- 
ference, 24; Nature of, 192; 
Rules of, 193; Undistributed 
Middle, 199; Illicit Major, 
199; Illicit Minor, 199; Aris- 
totle's Dictum, 208; Canons 
of, 209; Mathematical Axi- 
oms of, 210 ; Four Figures of, 
218; Moods of, 221; Incom- 
plete, 247. 

Syncategorematic Words, 48. 

Synthesis, Defined, 97; as a 
Method, 97. 

Synthetic Proposition, 138. 

T 

Teaching, Defined, 94; Com- 
pared with Instruction and 
Education, 95. 

Terms, Extension and Inten- 
sion of, 63; Used in Exten- 
sion and Intension, 65 ; which 
Cannot be Defined, 93; Con- 
tradictory and Opposite, 38; 
Logical, 47; Singular and 
General, 49; Collective and 
Distributive, 50; Concrete 
and Abstract. 51 : Connota- 
tive and Non-connotative, 
52; Positive and Negative, 
53; Contradictory and Oppo- 
site, 53; Privative and Nego- 
positive, 55; Absolute and 
Relative, 56. 



5oo 



Index 



Theory Defined, 96. 

Thinking, Definition of, 12; II 
lustration of Process, 13 
Compared with Knowing, 10 
Compared with Intuition, 2 
the Process, 12 ; Groups Many 
Into One, 18; in the Sensa- 
tion and Percept, 18; Evolu- 
tion and Thinking Mind, 19; 
of the Child, 20; of the 
Adult, 20; and the Concept, 
21 ; and the Judgment, 22 ; 
and Apprehension, 24; Stages 
in, 25; in the Inference, 24; 
Laws of, 32; Unity of Laws, 
40; Progressive, 465; Right, 
Necessity of, 466; Indiffer- 
ent and Careless, 467. 

Thought and Language, 47. 

Thought is King, 437. 

Traduction, 377. 

Training, Definition of, 95. 

Tree of Porphyry, 111. 

Truistic Proposition, 139. 

Truth Defined, 96. 



U 

Uberweg Quoted, 4. 

Undistributed Middle, 199; Il- 
lustration of, 214. 

Uniformity of Nature, 362. 

Universal Affirmative Proposi- 
tion, 140. 

Universal Causation, 361. 

Universal Negative Proposi- 
tion, 142. 

Universal Propositions, 126. 



Variations, Method of Con- 
comitant, 402. 

W 

Watts Quoted, 4. 
Weakened Conclusion, 224. 
Whately Quoted, 4. 
Word-signs of Categorical 
Propositions, 122. 



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